Universality class of absorbing phase transitions with a conserved field

Phase transitions in crowd dynamics of resource allocation

We define and study a class of resource allocation processes where gN agents, by repeatedly visiting N resources, try to converge to an optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density g of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents (g<1), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a nontrivial faster-is-slower effect.

Connecting the microdynamics to the emergent macrovariables: self-organized criticality and absorbing phase transitions in the Deterministic Lattice Gas

We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the 1/f spectra [Phys. Rev. Lett. 64, 3103 (1990)] arising according to the self-organized criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low-density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the deterministic lattice gas is in the Manna universality class of absorbing state phase transitions. This is in contrast to expectations in the literature that suggested that the entirely deterministic nature of the dynamics would put the model in a different universality class. To our knowledge this is the first fully deterministic member of the Manna universality class.

Influence of quenched disorder on absorbing phase transitions in the conserved lattice gas model

Motivated by the Harris criterion, the absorbing phase transitions of the conserved lattice gas (CLG) model were studied on lattices with a quenched disorder, i.e., on infinite percolation networks, in two and three dimensions. The Harris criterion suggests that, in a magnetic system, the pure fixed point will be unstable if the specific-heat exponent is positive. For the CLG model, the specific-heat exponent α calculated by the hyperscaling relation α=2-dν, where ν is the spatial correlation length exponent in d dimensions, will be positive in two dimensions if the value of ν obtained earlier by Lübeck and Heger is employed. On the other hand, it will be close to 0 if the more recent value by Lee and Lee is used and it is positive in three dimensions with the available value of ν. Extensive numerical simulations showed that, when the concentration of disordered sites is less than the critical concentration, the critical exponents were similar to those on a regular lattice both in two and three dimensions. When the concentration of disordered sites becomes critical, the density of active particles showed nonuniversal power-law behavior for all particle densities considered in both dimensions. These results were in contrast to the results for the diluted contact process. The cause of such a nonuniversal behavior was addressed.

Effects of excluded volume interaction on diffusion-reaction processes in crowded environments

In nonequilibrium phase transitions of reaction-diffusion processes, the irrelevance of excluded volume interaction for the critical properties generally has been accepted due to the rare probability of multiple occupancy at criticality. Moreover, this belief is common sense in scale-free (SF) networks, which correspond to infinite dimensional irregular structures. However, the conventional belief is not satisfied in crowded environments in which the total number of particles is preserved in time. In this paper, we show, by investigating a typical process for epidemic spreading in crowded environments, that excluded volume interaction indeed changes critical behaviors in one dimension and surprisingly even mean-field behaviors in SF networks.

Threshold-induced phase transition in kinetic exchange models

We study an ideal-gas-like model where the particles exchange energy stochastically, through energy-conserving scattering processes, which take place if and only if at least one of the two particles has energy below a certain energy threshold (interactions are initiated by such low-energy particles). This model has an intriguing phase transition in the sense that there is a critical value of the energy threshold below which the number of particles in the steady state goes to zero, and above which the average number of particles in the steady state is nonzero. This phase transition is associated with standard features like "critical slowing down" and nontrivial values of some critical exponents characterizing the variation of thermodynamic quantities near the threshold energy. The features are exhibited not only in the mean-field version but also in the lattice versions.

Facilitated asymmetric exclusion

We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is occupied, we determine the steady-state current and the distribution of cluster sizes on a ring. We show that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave. This unexpected rarefaction wave discontinuity occurs generally for facilitated exclusion processes.

Field theoretic treatment of an effective action for a model of catalyzed autoamplification

Reaction-diffusion models can exhibit continuous phase transitions in behaviors, and their dynamics at criticality often exhibit scalings with key parameters that can be characterized by exponents. While models with only a single field that transitions between absorbing and nonabsorbing states are well characterized and typically fall in the directed percolation universality class, the effects of coupling multiple fields remain poorly understood. We recently introduced a model which has three fields: one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field [Tchernookov, J. Chem. Phys. 130, 134906 (2009)]. Simulations suggested that this model is in a universality class distinct from other reaction-diffusion systems studied previously. Although the three fields give rise to interesting physics, they complicate analysis of the model with renormalization-group methods. Here, we show how to systematically simplify the action for this model such that analytical expressions for the exponents of this universality class can be obtained by standard means. We expect the approach taken here to be of general applicability in reaction-diffusion systems with coupled order parameters that display qualitatively different behaviors close to criticality.

Discontinuous phase transitions of conserved threshold transfer process with deterministic hopping

The deterministic conserved threshold transfer process, which is a variant of the conserved threshold transfer process modified in a way as that hopping of a particle is to be deterministic, is proposed. The critical behavior of the model is investigated in one, two, and four dimensions. It is found that the order parameter yields a discontinuous transition; i.e., the transition appears to be first ordered in all dimensions considered. The origin of such a discontinuous transition is investigated, considering clustering of active sites and accumulation of critical sites just before the steady state is reached.

Universality class of the reversible-irreversible transition in sheared suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behavior as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved directed percolation models. This leads to predictions for the scaling behavior of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.

Cusps, self-organization, and absorbing states

Elastic interfaces embedded in (quenched) random media exhibit metastability and stick-slip dynamics. These nontrivial dynamical features have been shown to be associated with cusp singularities of the coarse-grained disorder correlator. Here we show that annealed systems with many absorbing states and a conservation law but no quenched disorder exhibit identical cusps. On the other hand, similar nonconserved systems in the directed percolation class are also shown to exhibit cusps but of a different type. These results are obtained both by a recent method to explicitly measure disorder correlators and by defining an alternative new protocol inspired by self-organized criticality, which opens the door to easily accessible experimental realizations.

Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models

We introduce and solve a model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density. In this model, an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant. Particles from such active sites hop stochastically to their right. We show that both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely, directed percolation.

Irreversibility and self-organization in hydrodynamic echo experiments

We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organization, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.

Scaling exponents and transition behavior of the generalized conserved lattice gas model at zero temperature

We study a generalized conserved lattice gas model in two dimensions by introducing an effective temperature to the conserved lattice gas model, where the number of particles is conserved during the dynamical process. We apply Monte Carlo simulation with the Metropolis transition rate. At zero temperature we find two transition behaviors; one between the localized active states and absorbing states and the other between the localized active states and active states. With a different definition of the order parameter for the second transition behavior, we obtain the critical exponents at the transition point.

Validity of scaling relations in absorbing phase transitions with a conserved field

The two scaling relations in absorbing phase transitions, nu_||=beta/theta and z=nu_||/nu_(perpendicular), are studied for a conserved lattice gas model. The critical indices calculated elaborately from the all-sample average density of active particles appear to satisfy both relations. However, the exponent nu_(perpendicular) calculated from the surviving samples does not appear to be consistent with the value in the thermodynamic limit. This is in contrast with earlier observations [M. Rossi, Phys. Rev. Lett. 85, 1803 (2000); S. Lübeck and P. C. Heger, Phys. Rev. E. 68, 056102 (2003)], in that the former scaling relation was claimed to be violated.

Confirming and extending the hypothesis of universality in sandpiles

Stochastic sandpiles self-organize to an absorbing-state critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called the C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was claimed to be in the DP class despite the existence of a conservation law. We show, by means of careful numerical simulations as well as by constructing and analyzing a field theory, that (contrarily to what was previously thought) this sandpile is also in the C-DP or Manna class. This confirms the hypothesis of universality for stochastic sandpiles and gives rise to a fully coherent picture of self-organized criticality in systems with conservation. In passing, we obtain a number of results for the C-DP class and introduce a strategy to easily discriminate between DP and C-DP scaling.

Universality split in absorbing phase transition with conserved field on fractal lattices

The universality split in absorbing phase transition between the conserved lattice gas (CLG) model and the conserved threshold transfer process (CTTP) is investigated on a checkerboard fractal and on a Sierpinski gasket. The critical exponents theta, beta, nu||, and z, which are associated with, respectively, the density of active particles in time, the order parameter, the temporal correlation length, and the dynamics of active particles, are elaborately measured for two models on selected fractal lattices. The exponents for the CLG model are found to be distinctly different from those of the CTTP model on a checkerboard fractal, whereas the two models exhibit the same critical behavior on a Sierpinski gasket, indicating that the universality split between the two models occurs only on a checkerboard fractal. Such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice.

Absorbing-state phase transitions: exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary (QS) probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and betanu_(perpendicular)) with an accuracy of 0.06% or better; precise results are also obtained for the pair contact process. The QS distribution yields insights on the statistical entropy of these models. Preliminary application to a model in the stochastic sandpile class is also described.

Absorbing phase transition in a conserved lattice gas model in one dimension

We investigated the nonequilibrium phase transition of the conserved lattice gas model in one dimension using two update methods: i.e., the sequential update and the parallel update. We measured the critical indices of theta, beta, nu(parallel), and nu(perpendicular), and found that, for a parallel update, the exponents were delicately influenced by the hopping rule of active particles. When the hopping rule was designed to be symmetric, the results were found to be consistent with those of the sequential update. The exponents we obtained were precisely the same as the corresponding results of a recently presented lattice model of two species of particles with a conserved field in one dimension, in contrast with the authors' claim. We also found that one of the scaling relations known for absorbing phase transition is violated.

Absorbing phase transition in conserved lattice gas model on fractal lattices

We study the continuous phase transition of the conserved lattice gas (CLG) model from an active phase into an absorbing phase on two fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski gasket. In the CLG model, a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty. We estimate critical exponents theta, beta, nu||, and nu perpendicular, characterizing, respectively, the density of active particles in time, the order parameter, the temporal and spatial correlation lengths near the critical point, and the results are confirmed by off-critical scaling and finite size scaling. The order parameter exponent beta on a checkerboard fractal appears to lie between the one-dimensional (1D) value and two-dimensional (2D) value of the CLG model, while that on a Sierpinski gasket lies between the 1D and 2D values of the conserved threshold transfer process. Such a difference is manifested based on the intrinsic properties of the underlying fractal lattices.

Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality

We elucidate a long-standing puzzle about the nonequilibrium universality classes describing self-organized criticality in sandpile models. We show that depinning transitions of linear interfaces in random media and absorbing phase transitions (with a conserved nondiffusive field) are two equivalent languages to describe sandpile criticality. This is so despite the fact that local roughening properties can be radically different in the two pictures, as explained here. Experimental implications of our work as well as promising paths for future theoretical investigations are also discussed.

Sticky grains do not change the universality class of isotropic sandpiles

We revisit the sandpile model with "sticky" grains introduced by Mohanty and Dhar [Phys. Rev. Lett. 89, 104303 (2002)] whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models. While for directed models this conclusion is unquestionable, for isotropic models we present strong evidence that the asymptotic scaling in the self-organized regime (in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate) is, like other stochastic sandpiles, generically in the Manna universality class. This conclusion is drawn from extensive Monte Carlo simulations, and is strengthened by the analysis of the Langevin equations (proposed by the same authors to account for this problem), argued to converge upon coarse-graining to the well-established set of Langevin equations for the Manna class.

Classification of phase transitions in reaction-diffusion models

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of nonequilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the "coordinate"- to the "phase"-space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero "energy." We identify four families of topologically distinct classes of phase portraits stable upon renormalization group transformations.

Critical exponents for the restricted sandpile

I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems, but are consistent with recent predictions derived from a Langevin equation for stochastic sandpiles [Ramasco, Phys. Rev. E 69, 045105(R) (2004)]. This suggests that apparent violations of universality in one-dimensional sandpiles are due to strong corrections to scaling and finite-size effects.

Exact solution of the one-dimensional deterministic fixed-energy sandpile

By reason of the strongly nonergodic dynamical behavior, universality properties of deterministic fixed-energy sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be solved exactly, and provide a deeper understanding of the origin of the nonergodicity. By means of exact arguments, we prove the occurrence of orbits of well-defined periods and their dependence on the conserved energy density. Further statistical estimates of the size of the attraction's basins of the different periodic orbits lead to a complete characterization of the activity vs energy density phase diagram in the limit of large system's size.

Stationary distribution of finite-size systems with absorbing states

We introduce a procedure that allows us to obtain nontrivial stationary distributions of finite-size models with absorbing states. Two models are studied: the contact process and the sandpile model with height restriction. To avoid the permanence of the system in the absorbing state we create a small perturbation that drives the system out of the absorbing state. In the former model a particle is created, in the latter an active site is created. The stationary distributions around the critical point are analyzed by the use of finite-size scaling.

Simple sandpile model of active-absorbing state transitions

We study a simple sandpile model of active-absorbing state transitions in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold. We show that the active phase has product measure whereas nontrivial correlations are found numerically in the absorbing phase. It is argued that the system relaxes to the latter phase slower than exponentially. The critical behavior of this model is found to be different from that of the other known universality classes.

Absorbing phase transition with a conserved field

We study a lattice gas model where the number of particles is conserved during dynamical process. Our model shows a continuous phase transition from a fluctuating phase to two symmetric absorbing states at the critical point in one dimension. We conjecture the values of the critical exponents characterizing the phase transition of our model. We show that the obtained values are in good agreement with those estimated from computer simulations. The critical exponents indicate that our model exhibits an absorbing phase transition which is different from the known ones.

Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.

Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.

Conserved lattice gas model with infinitely many absorbing states in one dimension

The conserved lattice gas model with infinitely many absorbing states is studied on a chain and on a ladder. In both one-dimensional lattices it exhibits a phase transition from an absorbing phase to an active state. The model defined on a chain is solved exactly and shows a critical behavior with classical critical exponents. However, the model defined on a ladder shows a critical behavior, obtained from numerical simulation, that places the model in the same universality class as the Manna model.

Critical behavior of nonequilibrium continuous phase transition in A+BC catalytic reaction system

We study two lattice gas models for the A+BC-->AC+ 1/2 B2 reaction system. Model I includes the influences of the adsorbate diffusion and model II includes the effect of the diffusion and position exchange of B and C atoms. Model I exhibits a continuous phase transition with infinitely many absorbing states from a reactive state to a poisoned state of B and C atoms and a discontinuous transition to a poisoned state of A and B atoms when the fraction of A in the gas phase varies. The critical exponents are estimated accurately. The simulation results indicate clearly that the critical behavior of the continuous phase transition in model I belongs to the directed percolation (DP) universality class. Model II, however, exhibits a continuous transition with two absorbing states, and its critical behavior is obviously distinct from the DP universality class.

Critical behavior of the two-dimensional 2A-->3A, 4A--> phi binary system

The phase transitions of the recently introduced 2A-->3A, 4A--> phi reaction-diffusion model [G. Odor, Phys. Rev. E 69, 036112 (2004)]] are explored in two dimensions. This model exhibits site-occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion-creation rate space is confirmed, in agreement with cluster mean-field and one-dimensional results. For strong diffusion, a mean-field transition can be observed at zero branching rate characterized by an alpha=1/3 density decay exponent. In contrast, for weak diffusion the effective 2A-->3A-->4A--> phi reaction becomes relevant and the mean-field transition of the 2A-->3A, 2A--> phi model characterized by alpha=1/2 also appears for nonzero branching rates.

Directed fixed energy sandpile model

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.

Absorbing state phase transitions with quenched disorder

Quenched disorder--in the sense of the Harris criterion--is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for a weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

Violation of the Widom scaling law for effective crossover exponents

In this work we consider the universal crossover behavior of two nonequilibrium systems exhibiting a continuous phase transition. Focusing on the field driven crossover from mean-field to non-mean-field scaling behavior we show that the well-known Widom scaling law is violated for the effective exponents in the so-called crossover regime.

Numerical study of the Langevin theory for fixed-energy sandpiles

The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles and other self-organizing systems, is studied numerically. The equation is similar to the Reggeon field theory, describing generic systems with absorbing states, but it is coupled linearly to a second conserved and static (nondiffusive) field. It has been claimed to represent a different universality class, including different discrete models: the Manna as well as other sandpiles, reaction-diffusion systems, etc. In order to integrate the equation, and surpass the difficulties associated with its singular noise, we follow a numerical technique introduced by Dickman. Our results coincide remarkably well with those of discrete models claimed to belong to this universality class, in one, two, and three dimensions. This provides a strong backing for the Langevin theory of stochastic sandpiles, and to the very existence of this meagerly understood universality class.

Fluctuations and correlations in sandpiles and interfaces with boundary pinning

Interfaces are studied in an inhomogeneous critical state where boundary pinning is compensated with a ramped force. Sandpiles driven off the self-organized critical point provide an example of this ensemble in the Edwards-Wilkinson (EW) model of kinetic roughening. A crossover from quenched to thermal noise violates spatial and temporal translational invariances. The bulk temporal correlation functions have the effective exponents beta(1D) approximately 0.88+/-0.03 and beta(2D) approximately 0.52+/-0.05, while at the boundaries beta(b,1D/2D) approximately 0.47+/-0.05. The bulk beta(1D) is shown to be reproduced in a randomly kicked thermal EW model.

Universality class of absorbing transitions with continuously varying critical exponents

The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a different type of critical phenomenon distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

Universal finite-size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field

We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows one to validate certain hyperscaling relations. Using these hyperscaling relations it is possible to express the avalanche exponents of a self-organized critical system in terms of the ordinary exponents of a continuous absorbing phase transition.

Universal scaling behavior at the upper critical dimension of nonequilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.

Universal behavior of crossover scaling functions for continuous phase transitions

We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class; i.e., they are characterized by the same scaling functions and the same critical exponents. Varying the range of interactions, we examine the crossover from the mean-field-like to the non-mean-field scaling behavior. A phenomenological scaling form is applied in order to describe the full crossover region, which spans several decades. Our results strongly support the hypothesis that the crossover function is universal.

Nonequilibrium phase transition in a self-activated biological network

We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.

Universality class of nonequilibrium phase transitions with infinitely many absorbing states

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is d(c)=6, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an epsilon =6-d expansion.

Scaling behavior of the conserved transfer threshold process

We analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process. We determined the steady state scaling behavior of the order parameter as a function of both the control parameter and an external field, conjugated to the order parameter. The external field is realized as a spontaneous creation of active particles which drives the system away from criticality. The obtained results yield that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field.

n-site approximations and coherent-anomaly-method analysis for a stochastic sandpile

n-site cluster approximations for a stochastic sandpile in one dimension are developed. A height restriction is imposed to limit the number of states: each site can harbor at most two particles (height z(i)< or =2). (This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded.) On the basis of results for n< or =11 sites, the critical particle density as zeta(c)=0.930(1) is estimated, in good agreement with simulations. A coherent anomaly analysis yields estimates for the order parameter exponent [beta=0.41(1)] and the relaxation time exponent (nu(//) approximately 2.5).

Well-defined set of exponents for a pair contact process with diffusion

Recently it was suggested that a pair contact process with diffusion (PCPD) might represent an independent new universality class different from the directed percolation (DP) and the parity conservation (PC) class. The dynamics in the PCPD are usually controlled by two independent parameters. The critical exponents for the PCPD are known to have different values for varying values of the two independent parameters. However, once the diffusion and annihilation (or coagulation) rate in the PCPD is tuned in a way that the process without offspring production is exactly solvable, a well-defined set of the exponents for the PCPD is obtained. Then dynamics are controlled by only one independent parameter. The obtained critical exponents are different than those of DP and PC. The critical exponents satisfy the generalized hyperscaling relation within numerical errors.