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

Abstract

Scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is still lacking, which is of our interest in this study. There are three different routes from the DI to the DP classes by introducing a symmetry breaking field (SB), breaking a modulo 2 conservation (CB), or making channels connecting two equivalent absorbing states (CC). Each route can be characterized by a crossover exponent, which is found numerically as $\varphi =2.1\pm 0.1$ (SB), $4.6\pm 0.2$ (CB), and $2.9\pm 0.1$ (CC), respectively. The difference between the SB and CB crossover can be understood easily in the domain wall language, while the CC crossover involves an additional critical singularity in the auxiliary field density with the memory effect to identify itself independent.

7 pages, 6 figures

References in corpus (34)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Theory of Branching and Annihilating Random Walks
• Field Theory of Branching and Annihilating Random Walks
• Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring
• Langevin description of critical phenomena with two symmetric absorbing states
• Stochastic Lattice Models with Several Absorbing States
• One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk
• Absorbing Phase Transitions of Branching-Annihilating Random Walks
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model
• Dynamic scaling behavior of an interacting monomer--dimer model
• Novel universality class of absorbing transitions with continuously varying critical exponents
• Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks
• Critical phenomena of nonequilibrium dynamical systems with two absorbing states
• Critical behavior of an absorbing phase transition in an interacting monomer-dimer model
• Reentrant phase diagram of branching annihilating random walks with one and two offsprings
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Binary spreading process with parity conservation
• The three species monomer-monomer model: A mean-field analysis and Monte Carlo study
• Epidemic processes with immunization
• Driven Pair Contact Process with Diffusion
• The phase transition of the diffusive pair contact process revisited
• The relaxation of initial condition in systems with infinitely many absorbing states
• A parity conserving dimer model with infinitely many absorbing states
• Crossover from the pair contact process with diffusion to directed percolation
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• Interacting Monomer-Dimer Model with Infinitely Many Absorbing States
• Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion
• Generating function, path integral representation, and equivalence for stochastic exclusive particle systems
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Crossovers from parity conserving to directed percolation universality
• Dynamic behavior of driven interfaces in models with two absorbing states
• Directed Ising type dynamic preroughening transition in one dimensional interfaces

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• Universality classes of absorbing phase transitions in generic branching-annihilating particle systems
• Crossover from the parity-conserving pair contact process with diffusion to other universality classes
• Generalized contact process with two symmetric absorbing states in two dimensions
• Order-disorder transition in a model with two symmetric absorbing states
• Crossover behaviors in branching annihilating attracting walk
• Phase transitions of the generalized contact process with two absorbing states
• Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states
• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion
• Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice