Universality classes of absorbing phase transitions in generic branching-annihilating particle systems

Abstract

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 $\epsilon$. For $\epsilon =0$, 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 $\epsilon$ does not change the DP universality class but alters the other two universality classes. For non-zero $\epsilon$, the PCPD class crosses over to DP and the PC class changes to a new universality class.

arXiv comment5 pages, 7 figures

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• One-dimensional annihilating random walk with long-range interaction
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• Absorbing phase transitions in a non-conserving sandpile model
• Tagged particle dynamics in one dimensional $A+A\to kA$ models with the particles biased to diffuse towards their nearest neighbour
• $A+A\to \varnothing$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates
• 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
• Effect of presence of rigid impurities in a system of annihilating domain walls with dynamic bias