Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior

TL;DR

This paper develops a unified approach to connect microscopic spin dynamics with macroscopic behavior in systems with two symmetric absorbing states, explaining coarsening and phase transitions through derived Langevin equations.

Contribution

It introduces a general method to derive Langevin equations from microscopic dynamics, linking local rules to global phase transition types in spin models.

Findings

Macroscopic behavior depends only on first derivatives of spin-flip probabilities.

The approach explains coarsening in nonlinear voter models.

Monte Carlo simulations agree with theoretical predictions.

Abstract

We propose a general approach to study spin models with two symmetric absorbing states. Starting from the microscopic dynamics on a square lattice, we derive a Langevin equation for the time evolution of the magnetization field, that successfully explains coarsening properties of a wide range of nonlinear voter models and systems with intermediate states. We find that the macroscopic behavior only depends on the first derivatives of the spin-flip probabilities. Moreover, an analysis of the mean-field term reveals the three types of transitions commonly observed in these systems -generalized voter, Ising and directed percolation-. Monte Carlo simulations of the spin dynamics qualitatively agree with theoretical predictions.