Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter

TL;DR

This paper investigates corrections to scaling in phase-ordering dynamics of vector systems with O(n) symmetry, deriving correction exponents and functions using Gaussian closure theory and exact solutions for specific models.

Contribution

It introduces a detailed analysis of correction-to-scaling exponents and functions for vector order parameters, extending understanding beyond leading scaling behavior.

Findings

Correction-to-scaling exponent omega depends on system dimensionality and order parameter components.

Derived correction functions for both conserved and nonconserved systems.

Provided exact correction results for the 1-d XY model.

Abstract

Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal-time pair correlation function has the form C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length scale. The correction-to-scaling exponent, omega, and the correction-to-scaling function, f_1(x), are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general, omega is a non-trivial exponent which depends on both the dimensionality, d, of the system and the number of components, n, of the order parameter. Corrections to scaling are also calculated for the nonconserved 1-d XY model, where an exact solution is possible.