Corrections to scaling in phase-ordering dynamics of two-dimensional xy system

Abstract

Scaling phenomena in nonequilibrium dynamics are very important and challenging problem in condensed matter physics. In this thesis, we investigated the scaling phenomena in phase-ordering dynamics. The purpose of the thesis is to determine dynamical scaling properties and its correction forms in phase-ordering dynamics of two-dimensional XY system. We consider quenches in nonconserved two-dimensional XY system between any two temperatures below the Kosterlitz-Thouless transition temperature. The first-order correction to correlations associated with the amplitude fluctuations is investigated. In order to solve this problem, we treat the small amplitude fluctuations comparing to the phase fluctuations. Then, the dynamics of phase and amplitude fields become uncoupled. The dynamics of the phase field is refered as the zeroth-order theory while for the amplitude field is refered as the first-order correction. We find that, at late times, the nonequilibrium parts of both zeroth- and first-order correlations exhibit scaling.