Algebraic coarsening in voter models with intermediate states

TL;DR

This paper studies how adding intermediate states to the voter model changes its coarsening behavior, leading to algebraic decay of interfaces and effective surface tension, analyzed through Langevin equations and confirmed by simulations.

Contribution

It introduces a field-theoretic approach to analyze voter models with intermediate states, revealing a transition from logarithmic to algebraic coarsening.

Findings

Algebraic decay of interface density in modified voter models.

Effective surface tension emerges due to intermediate states.

Good agreement between theoretical analysis and lattice simulations.

Abstract

The introduction of intermediate states in the dynamics of the voter model modifies the ordering process and restores an effective surface tension. The logarithmic coarsening of the conventional voter model in two dimensions is eliminated in favour of an algebraic decay of the density of interfaces with time, compatible with Model A dynamics at low temperatures. This phenomenon is addressed by deriving Langevin equations for the dynamics of appropriately defined continuous fields. These equations are analyzed using field theoretical arguments and by means of a recently proposed numerical technique for the integration of stochastic equations with multiplicative noise. We find good agreement with lattice simulations of the microscopic model.