Langevin description of critical phenomena with two symmetric absorbing states

TL;DR

This paper introduces a Langevin equation to model critical phenomena with two symmetric absorbing states, clarifying phase transitions and their relation to voter, Ising, and directed percolation universality classes.

Contribution

It proposes a novel Langevin framework for symmetric absorbing states and elucidates the nature of phase transitions, including the splitting into Ising and directed percolation in higher dimensions.

Findings

The Langevin model captures the phase diagram of systems with two symmetric absorbing states.

The direct transition is characterized as a generalized voter critical point.

In dimensions >1, the transition splits into Ising and directed percolation types.

Abstract

On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transitions in dimensions larger than one.