Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models

TL;DR

This paper investigates a two-parameter class of stochastic processes in two dimensions, interpolating between the Ising, voter, and majority vote models, analyzing their coarsening dynamics and persistence properties through simulations.

Contribution

It introduces a unified framework for these models and measures their persistence behavior, revealing a consistent power-law decay with an exponent around 0.22.

Findings

Persistence probability decays as a power law with exponent ~0.22

The models interpolate between well-known models like Ising and voter

Persistence is related to the nature of domain interfaces

Abstract

We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the plane of parameters correspond to the Ising model, voter model and majority vote model. The dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing, annihilating, and branching random walkers. We use the freedom allowed by the space of parameters to measure, by numerical simulations, the persistence probability of a generic model in the low temperature phase, where the system coarsens. This probability is found to decay at large times as a power law with a seemingly constant exponent $\theta\approx 0.22$. We also discuss the connection between persistence and the nature of the interfaces between domains.