Reentrant phase diagram of branching annihilating random walks with one and two offsprings

TL;DR

This paper explores the phase diagram of one-dimensional branching annihilating random walks with one and two offsprings, revealing a reentrant transition driven by static reflection symmetry, challenging conventional expectations.

Contribution

It uncovers a reentrant phase transition in branching annihilating random walks caused by static reflection symmetry, contrasting with traditional dynamic symmetry assumptions.

Findings

Reentrant phase transition observed as the two-offspring branching rate increases.

Static reflection symmetry explains the reentrant behavior.

Conventional wisdom is recovered when dynamic reflection symmetry is considered.

Abstract

We investigate the phase diagram of branching annihilating random walks with one and two offsprings in one dimension. A walker can hop to a nearest neighbor site or branch with one or two offsprings with relative ratio. Two walkers annihilate immediately when they meet. In general, this model exhibits a continuous phase transition from an active state into the absorbing state (vacuum) at a finite hopping probability. We map out the phase diagram by Monte Carlo simulations which shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two-offspring branching process increases. This reentrant property apparently contradicts the conventional wisdom that increasing the number of offsprings will tend to make the system more active. We show that the reentrant property is due to the static reflection symmetry of two-offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one.