On large deviations of interface motions for statistical mechanics models

TL;DR

This paper investigates the large deviations of interface motions in statistical mechanics models, deriving explicit formulas for the limiting functionals that describe deviations from mean curvature flow in Glauber dynamics and Kawasaki processes.

Contribution

It provides explicit formulas for the mobility and transport coefficients in the large deviations functional for interface motions in Ising and related models.

Findings

Explicit formulas for mobility and transport coefficients.

Large deviations asymptotics linked to mean curvature flow.

Analysis applies to Glauber and Kawasaki dynamics.

Abstract

We discuss the sharp interface limit of the action functional associated to either the Glauber dynamics for Ising systems with Kac potentials or the Glauber+Kawasaki process. The corresponding limiting functionals, for which we provide explicit formulae of the mobility and transport coefficients, describe the large deviations asymptotics with respect to the mean curvature flow.