Critical phenomena of nonequilibrium dynamical systems with two absorbing states

Abstract

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only.

11 pages, 21 figures, Revtex, submitted to Phy. Rev. E

Cited by in corpus (33)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Absorbing-state phase transitions in fixed-energy sandpiles
• Langevin description of critical phenomena with two symmetric absorbing states
• Non-perturbative fixed point in a non-equilibrium phase transition
• Novel universality class of absorbing transitions with continuously varying critical exponents
• Nature of phase transitions in a probabilistic cellular automaton with two absorbing states
• Binary spreading process with parity conservation
• Critical behavior of the contact process in annealed scale-free networks
• Branching and annihilating Levy flights
• Does hardcore interaction change absorbing type critical phenomena?
• Surface Critical Behavior in Systems with Absorbing States
• Anomalous Roughness in Dimer-Type Surface Growth
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• Interacting Monomer-Dimer Model with Infinitely Many Absorbing States
• Anomalous Roughness, Localization, and Globally Constrained Random Walks
• Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Three different routes from the directed Ising to the directed percolation class
• Crossover from the parity-conserving pair contact process with diffusion to other universality classes
• Persistence as Order Parameter in Generalized Pair Contact Process with Diffusion
• Crossovers from parity conserving to directed percolation universality
• Order-disorder transition in a model with two symmetric absorbing states
• Directed Ising type dynamic preroughening transition in one dimensional interfaces
• Crossover behaviors in branching annihilating attracting walk
• Dynamic behavior of driven interfaces in models with two absorbing states
• Stability of vacuum in coupled directed percolation processes
• Generalized scaling relations for unidirectionally coupled nonequilibrium systems
• Systems with superabsorbing states
• Collective Helping and Bystander Effects in Coevolving Helping Networks
• Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states
• Double transitions, non-Ising criticality and critical absorbing phase in an interacting monomer-dimer model on a square lattice:
• Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors