Voter models with conserved dynamics

TL;DR

This paper introduces a modified voter model with local conservation laws, revealing faster phase ordering and algebraic domain growth in two dimensions, contrasting with standard voter model behavior.

Contribution

The study presents a novel voter model with conserved magnetization, demonstrating accelerated phase ordering and a new scaling regime in two-dimensional systems.

Findings

Local conservation speeds up phase ordering

Algebraic domain growth observed

Phenomenological model accurately predicts dynamics

Abstract

We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding up the phase ordering process. The system is shown to exhibit a scaling regime characterized by algebraic domain growth, at odds with the logarithmic coarsening of the standard voter model. A phenomenological approach based on cluster diffusion and similar to Smoluchowski ripening correctly predicts the observed scaling regime. Our analysis exposes unexpected complexity in the phase ordering dynamics without thermodynamic potential.