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

Abstract

The pair contact process with diffusion (PCPD) with modulo 2 conservation (\pcpdt) [$2A\to 4A$, $2A\to 0$] 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 \pcpdt shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the \pcpdt to the DI is studied by including a parity-conserving single-particle process ($A\to 3A$). 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 $A\to 2A$. 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 [$3A\to 5A$, $2A\to 0$] to the DI by adding $A\to 3A$. 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 \pcpdt 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.

8 pages, 8 figures

References in corpus (12)

• The non-equilibrium phase transition of the pair-contact process with diffusion
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Driven Pair Contact Process with Diffusion
• The phase transition of the diffusive pair contact process revisited
• Crossover from the pair contact process with diffusion to directed percolation
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• Universality class of the pair contact process with diffusion
• 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
• Three different routes from the directed Ising to the directed percolation class
• Monte Carlo simulations of bosonic reaction-diffusion systems and comparison to Langevin equation description

Cited by in corpus (10)

• Finite scale singularity in the renormalization group flow of a reaction-diffusion system
• Critical decay exponent of the pair contact process with diffusion
• Universality classes of absorbing phase transitions in generic branching-annihilating particle systems
• Generalized contact process with two symmetric absorbing states in two dimensions
• Order-disorder transition in a model with two symmetric absorbing states
• Branching annihilating random walks with long-range attraction in one dimension
• Phase transitions of the generalized contact process with two absorbing states
• Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension
• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice