Non-equilibrium Phase-Ordering with a Global Conservation Law

TL;DR

This paper investigates non-equilibrium phase ordering in a quenched Ising model with global conservation laws, comparing infinite-range Kawasaki dynamics and the microcanonical Creutz algorithm, revealing different growth laws.

Contribution

It introduces the microcanonical Creutz algorithm as a better implementation of global conservation, restoring standard growth laws across temperatures.

Findings

Infinite-range Kawasaki dynamics leads to anomalous growth laws.

The microcanonical Creutz algorithm exhibits standard growth behavior.

Energy transport mechanisms differ between the two methods.

Abstract

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.