Stationary definition of persistence for finite temperature phase ordering

TL;DR

This paper investigates the persistence properties of the two-dimensional kinetic Ising model at finite temperature, focusing on the limiting distribution of local magnetisation and the associated persistence and first passage exponents.

Contribution

It introduces a stationary definition of persistence for finite temperature phase ordering and analyzes the temperature dependence of related exponents.

Findings

Limiting distribution of local magnetisation is singular at spontaneous magnetization values.

Persistence exponent is defined via the singularity exponent.

First passage exponents vary with temperature.

Abstract

For the two dimensional kinetic Ising model at finite temperature, the local mean magnetisation $M_t=t^{-1}\int_{0}^t\sigma(t')\d t'$, simply related to the fraction of time spent by a given spin in the positive direction, has a limiting distribution, singular at $\pm m_0(T)$, the Onsager spontaneous magnetization. The exponent of this singularity defines the persistence exponent $\theta$. We also study first passage exponents associated to persistent large deviations of $M_t$, and their temperature dependence.