Domain Number Distribution in the Nonequilibrium Ising Model

TL;DR

This paper investigates the distribution and survival probabilities of domains in a one-dimensional Ising model under specific dynamics, introducing an approximation method that accurately estimates key distribution characteristics.

Contribution

The study introduces an independent interval approximation to accurately estimate domain length and number distributions in the nonequilibrium Ising model.

Findings

Survival probability decays as t^{-\psi} with a nontrivial exponent.

Unreacted domain probability decays as t^{-\delta} with a distinct exponent.

Approximation method closely matches numerical and analytical results.

Abstract

We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain, $Q_1(t)\sim t^{-\delta}$, are characterized by two independent nontrivial exponents. We develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents.