Universality class of absorbing phase transitions with a conserved field

Sandpiles with height restrictions

We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of particles per site), cannot exceed two. This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded. Two toppling rules are considered: in one, the particles are redistributed independently, while the other involves some cooperativity. We study the fixed-energy system (no input or loss of particles) using cluster approximations and extensive simulations, and find that it exhibits a continuous phase transition to an absorbing state at a critical value zeta(c) of the particle density. The critical exponents agree with those of the unrestricted Manna sandpile.

Simple absorbing-state transition

We study a simple reaction-diffusion process that exhibits a phase transition to an absorbing phase in its steady state. We characterize the universal properties of the transition by computing the associated critical exponents. We suggest that the exclusion constraint between particles may change the universality class of the transition even though the density is asymptotically low at the transition. This is surprising as no segregation or jamming phenomena are in play since we are dealing with a single species diffusing without drift.

Scaling behavior of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension

We analyze numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field. The external field is realized as a spontaneous creation of active particles that drives the system away from criticality. Nevertheless, the order parameter obeys certain scaling laws for sufficiently small external fields. These scaling laws are investigated and the corresponding exponents are determined in various dimensions (D=2,3,4,5). At the so-called upper critical dimension D(c)=4 one has to modify the usual scaling laws by logarithmic corrections.

Criticality and oscillatory behavior in non-Markovian contact process

A non-Markovian generalization of a one-dimensional contact process is being introduced in which every particle has an age and will be annihilated at its maximum age tau. There is an absorbing state phase transition which is controlled by this parameter. The model can demonstrate oscillatory behavior in its approach to the stationary state. These oscillations are also present in the mean-field approximation, which is a first-order differential equation with time delay. Studying dynamical critical exponents suggests that the model belongs to the direct percolation universality class.

Multicomponent binary spreading process

I investigate numerically the phase transitions of two-component generalizations of binary spreading processes in one dimension. In these models pair annihilation AA --> emptyset, BB --> emptyset, explicit particle diffusion, and binary pair production processes compete with each other. Several versions with spatially different production are explored, and it is shown that for the cases 2A --> 3A, 2B--> 3B and 2A --> 2AB, 2B--> 2BA a phase transition occurs at zero production rate (sigma=0), which belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent beta=2. In the model with particle production AB --> ABA, BA --> BAB a phase transition point can be located at sigma(c)=0.3253 which belongs to the class of one-component binary spreading processes.

Interface depinning versus absorbing-state phase transitions

According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and order parameter coupled to a nondiffusive conserved field coincide with those of the linear interface depinning model within computational accuracy. In this paper the connection between absorbing-state phase transitions and interface pinning in quenched disordered media is investigated. For that, we present an heuristic mapping of the interface dynamics in a disordered medium into a Langevin equation for the active-site density and show that a Reggeon-field-theory-like description, in which the order parameter appears coupled to an additional nondiffusive conserved field, emerges rather naturally. Reciprocally, we construct a mapping from a discrete model belonging in the absorbing state with a conserved-field class to a discrete interface equation, and show how a quenched disorder, typical of the interface representation is originated. We discuss the character of the possible noise terms in both representations, and overview the critical exponent relations. Evidence is provided that, at least for dimensions larger that one, both universality classes are just two different representations of the same underlying physics.

First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results

First-order irreversible phase transitions (IPT's) between an active regime and an absorbing state are studied in a single-component, two-dimensional interacting particle system by means of both simulations and a mean-field analysis. Several features obtained using the mean-field approximation such as the presence of a first-order IPT and hysteresis effects, are in excellent agreement with simulation results. In addition, extensive epidemic simulations show that the dynamical critical behavior of the system is by no means scale invariant.

Critical behavior of a one-dimensional fixed-energy stochastic sandpile

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles) of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value of the particle density, and exhibits the hallmarks of an absorbing-state phase transition, including finite-size scaling. Critical exponents are obtained from extensive simulations, which treat stationary and transient properties, and an associated interface representation. These exponents characterize the universality class of an absorbing-state phase transition with a static conserved density in one dimension; they differ from those expected at a linear-interface depinning transition in a medium with point disorder, and from those of directed percolation.

Criticality of natural absorbing states

We study a recently introduced ladder model that undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behavior of the model is the same as that of the branching-annihilating random walk with N>/=2 species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power-law singularities that signal the approach of the critical point. These results are also explained using random-walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum-finding procedure, it has the best efficiency very close to the critical point.

Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension

We analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field [Phys. Rev. Lett. 85, 1803 (2000)]. We determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in D=2,3,4,5 dimensions. A comparison of our results and those obtained from a mean-field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four.

Critical behavior of a nonequilibrium system with two nonordering conserved fields

We investigate the critical behavior of a nonequilibrium system with two particle species A and B that exhibits a continuous absorbing-state phase transition. The number of particles of each species (N(A) and N(B)) is conserved by the dynamical process. Numerical results show that the order parameter exponent beta depends on the ratio N(B)/N(A) at criticality. Some aspects of critical dynamic behavior are also studied, namely, the decay of the active density at criticality and the critical spreading of a perturbation to an absorbing configuration. Anomalies in the relaxation are associated with the presence of different time scales in the dynamics of the model.

Nonequilibrium model for the contact process in an ensemble of constant particle number

We introduce and analyze numerically a nonequilibrium model with a conserved dynamics which is a realization of the contact process in an ensemble of constant particle number. The model possesses just one process in which particles jump around landing only on empty sites next to an existing particle. Particles are not allowed to land on a vacant site surrounded by empty sites. In contrast with the ordinary contact process, the present model does not have an absorbing state. In spite of lacking an absorbing state, the model displays properties that, in the thermodynamic limit, are identical to those of the ordinary contact process.

One-dimensional contact process: duality and renormalization

We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.

Field theory for reaction-diffusion processes with hard-core particles

We show how to build up a systematic bosonic field theory for a general reaction-diffusion process involving hard-core particles in arbitrary dimension. We discuss a recent approach proposed by Park, Kim, and Park [Phys. Rev. E 62, 7642 (2000)]. As a test bench for our method, we show how to recover the equivalence between asymmetric diffusion of excluding particles and the noisy Burgers equation.

Field theory of absorbing phase transitions with a nondiffusive conserved field

We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a nondiffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class.