Identification of domain walls in coarsening systems at finite temperature

TL;DR

This paper extends a numerical method to identify domain walls in coarsening systems at finite temperature, enabling precise measurement of domain surface areas in the 2D Ising model and analyzing algorithmic dependencies.

Contribution

It introduces a three-replica extension of Derrida's method to clearly identify domain walls in finite-temperature coarsening systems.

Findings

Successfully measures domain surface area in 2D Ising model

Demonstrates the method's robustness against different algorithms

Provides insights into domain wall dynamics at finite temperature

Abstract

Recently B. Derrida [Phys. Rev. E 55, 3705 (1997)] introduced a numerical technique that allows one to measure the fraction of persistent spins in a coarsening nonequilibrium system at finite temperature. In the present work we extend this method in a way that domain walls can be clearly identified. To this end we consider three replicas instead of two. As an application we measure the surface area of coarsening domains in the two-dimensional Ising model at finite temperature. We also discuss the question to what extent the results depend on the algorithmic implementation.