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Herald of Omsk University Series Psychology

Исследование эффектов старения в двумерной XY-модели

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Sergey V. Alekseev

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The ageing phenomena in two-dimensional XY model are investigated at low temperatures through Monte-Carlo methods starting from the ordered state. The two-time correlation function and spin-spin correlation function are measured.

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With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.
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With Monte Carlo simulation method,the aging phenomenon of the 2D XY model is numerically studied.Starting from an ordered initial state,the system is suddenly quenched to critical temperature Tc.The two-time autocorrelation function A(t,t') is measured.For a dynamic process with an ordered initial state,the difficult problem is that accurate analysis is lagging behind the Monte Carlo simulation study.So many activities have been devoted to dynamic scaling form.According to the numerical experimental data of 2D XY non-equilibrium system,the relation between A(t,t') and ratio of spatial correlation length is detected.The aging phenomenon exhibits a dynamic scaling behavior induced by the time correlation.The aging phenomenon is characterized by the dynamic scale invariance.The aging phenomenon of 2D XY model is confirmed.Especially,the correction of scaling behavior is numerically verified,the form of dynamic scaling of A(t,t') is more creditable than existing literatures.For a dynamic process starting from an ordered initial state,the scaling form assumption fits the numerical data well.The scaling form holds not only at lower temperatures but also around Tc.This is because of the simulation temperature is close to the critical temperature.Based on the dynamic scaling,the experimental data indicate that more accurate values of the critical exponents can be obtained.In addition,the data collapse phenomenon is observed.
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