Corrections to Scaling in Phase-Ordering Kinetics

TL;DR

This paper investigates the leading correction to scaling in phase-ordering kinetics, deriving explicit correction exponents and functions for various models, enhancing understanding of non-ideal initial conditions.

Contribution

It provides explicit calculations of correction-to-scaling exponents and functions for several soluble models of phase-ordering kinetics, including new results for the Mazenko theory.

Findings

Correction-to-scaling exponent =4 for d=1 Glauber and n-vector models.

For Mazenko theory, =3.8836 in 2D and 3.9030 in 3D.

Explicit forms of correction-to-scaling functions f_1(x) are derived.

Abstract

The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent \omega has the value \omega=4 for the d=1 Glauber model, the n-vector model with n=\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for d=3. The correction-to-scaling functions f_1(x) are also calculated.