Crossover behaviors in branching annihilating attracting walk

Abstract

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 [B. Daga and P. Ray, Phys. Rev. E {\bf 99}, 032104 (2019)]. 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.

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Cited by in corpus (6)

• Branching annihilating random walks with long-range attraction in one dimension
• One-dimensional annihilating random walk with long-range interaction
• $A+A\to \varnothing$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates
• Effect of presence of rigid impurities in a system of annihilating domain walls with dynamic bias
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice
• Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors