Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

TL;DR

This paper applies finite-size scaling to domain growth in the 2-D kinetic Ising model, using Monte Carlo simulations to analyze distribution functions and accurately determine growth exponents despite finite-size effects.

Contribution

It introduces a finite-size scaling ansatz for the order parameter distribution and demonstrates its effectiveness in analyzing domain growth in the kinetic Ising model.

Findings

Finite-size scaling accurately determines bulk growth exponents.

Distribution functions reveal configurational self-similarity.

Common domain size measures can underestimate finite-size effects.

Abstract

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.