Three different routes from the directed Ising to the directed percolation class

Crossover behaviors in branching annihilating attracting walk

We introduce branching annihilating attracting walk (BAAW) in one dimension. The attracting walk is implemented by a biased hopping in such a way that a particle prefers hopping to a nearest neighbor located on the side where the nearest particle is found within the range of attraction. We study the BAAW with four offspring by extensive Monte Carlo simulation. At first, we find the critical exponents of the BAAW with infinite range of attraction, which are different from those of the directed Ising (DI) universality class. Our results are consistent with the recent observation [Daga and Ray, Phys. Rev. E 99, 032104 (2019)2470-004510.1103/PhysRevE.99.032104]. Then, by studying crossover behaviors, we show that as far as the range of attraction is finite the BAAW belongs to the DI class. We conclude that the origin of non-DI critical behavior of the BAAW with infinite range of attraction is the long-range nature of the attraction.

Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent β of absorbing phase transitions in systems with two symmetric absorbing states. The value of β was conjectured to be 13/14≈0.93 and Monte Carlo simulation studies in the literature have repeatedly reproduced values consistent with the conjecture. In this paper, we systematically estimate β by analyzing the effective exponent after finding how strong corrections to scaling are. We show that the widely accepted numerical value of β is not correct. Rather, we obtain β=1.020(5) from different models with two symmetric absorbing states.

Universality classes of absorbing phase transitions in generic branching-annihilating particle systems with nearest-neighbor bias

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one-dimensional ring, where the walkers hop to their nearest neighbor with a bias ε. For ε=0, three universality classes-directed percolation (DP), parity-conserving (PC), and pair contact process with diffusion (PCPD)-are typically observed in such systems. We find that the introduction of ε does not change the DP universality class but alters the other two universality classes. For nonzero ε, the PCPD class crosses over to DP, and the PC class changes to a new universality class.

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)PHYADX0378-437110.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

Order-disorder transition in a model with two symmetric absorbing states

We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is around the order-disorder transition, and we investigate whether this transition is described by the critical exponents of the two-dimensional Ising model. By analyzing the relaxation dynamics of "staggered magnetization," the finite-size scaling, and the behavior of the magnetization in the presence of a symmetry-breaking field, we show that this model should belong to the Ising universality class. Our results along with the universality hypothesis support the idea that the order-disorder transition in two-dimensional models with two symmetric absorbing states is of the Ising universality class, contrary to the recent claim [K. Nam et al., J. Stat. Mech.: Theory Exp. (2011) L06001]. Furthermore, we illustrate that the Binder cumulant could be a misleading guide to the critical point in these systems.

Generalized contact process with two symmetric absorbing states in two dimensions

We explore the two-dimensional generalized contact process with two absorbing states by means of large-scale Monte-Carlo simulations. In part of the phase diagram, an infinitesimal creation rate of active sites between inactive domains is sufficient to take the system from the inactive phase to the active phase. The system, therefore, displays two different nonequilibrium phase transitions. The critical behavior of the generic transition is compatible with the generalized voter universality class, implying that the symmetry-breaking and absorbing transitions coincide. In contrast, the transition at zero domain-boundary activation rate is not critical.

Phase transitions of the generalized contact process with two absorbing states

We investigate the generalized contact process with two absorbing states in one space dimension by means of large-scale Monte Carlo simulations. Treating the creation rate of active sites between inactive domains as an independent parameter leads to a rich phase diagram. In addition to the conventional active and inactive phases we find a parameter region where the simple contact process is inactive, but an infinitesimal creation rate at the boundary between inactive domains is sufficient to take the system into the active phase. Thus, the generalized contact process has two different phase transition lines. The point separating them shares some characteristics with a multicritical point. We also study in detail the critical behaviors of these transitions and their universality.

Crossover from the parity-conserving pair contact process with diffusion to other universality classes

The pair contact process with diffusion (PCPD) with modulo 2 conservation (PCPD2) [ 2A-->4A , 2A-->0 ] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the directed percolation (DP). First, we show that the PCPD2 shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the PCPD2 to the DI is studied by including a parity-conserving single-particle process (A-->3A) . We find the crossover exponent 1/varphi_{1}=0.57(3) , which is argued to be identical to that of the PCPD-to-DP crossover by adding A-->2A . This suggests that the PCPD universality class has a well-defined fixed point distinct from the DP. Third, we study the crossover from a hybrid-type reaction-diffusion process belonging to the DP [ 3A-->5A , 2A-->0 ] to the DI by adding A-->3A . We find 1/varphi_{2}=0.73(4) for the DP-to-DI crossover. The inequality of varphi_{1} and varphi_{2} further supports the non-DP nature of the PCPD scaling. Finally, we introduce a symmetry-breaking field in the dual spin language to study the crossover from the PCPD2 to the DP. We find 1/varphi_{3}=1.23(10) , which is associated with a new independent route from the PCPD to the DP.