Domain Coarsening in 2-d Ising Model: Finite-Size Scaling for Conserved Dynamics

TL;DR

This paper investigates how finite system size affects domain growth kinetics in a 2D Ising model, confirming the Lifshitz-Slyozov theory exponent through Monte Carlo simulations across various system sizes.

Contribution

It provides a precise estimate of the domain growth exponent in 2D Ising models and demonstrates the early onset and persistence of LS theory predictions in finite systems.

Findings

The growth exponent is approximately 1/3, matching LS theory.

LS exponent appears early and holds until domains reach three quarters of equilibrium size.

Finite-size effects are quantified in the domain growth process.

Abstract

We quantify the effect of system size in the kinetics of domain growth in Ising model with 50:50 composition in two spatial dimensions. Our estimate of the exponent, $\alpha=0.334\pm0.004$, for the power law growth of linear domain size, from Monte Carlo simulation using small systems of linear dimensions L=16, 32, 64, and 128, is in excellent agreement with the prediction of Lifshitz-Slyozov (LS) theory, $\alpha=1/3$. We find that the LS exponent sets in very early and continues to be true until average size of domains reaches three quarters of equilibrium limit.