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The Physics of Metals and Metallography

Investigation of the effects of aging and temperature dependence of the transverse rigidity of a system in the two-dimensional XY model

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Sergey V. Alekseev, Ivan S Popov

Published Dec 1, 2014• 17 citations
Publisher

Abstract

The phenomenon of aging in the low-temperature nonequilibrium critical behavior of the two-dimensional XY model has been investigated by the Monte Carlo methods from different initial states. The temperature dependence of the transverse rigidity in the low-temperature critical behavior of the two-dimensional XY model has been investigated by the Monte Carlo methods.

DOI
10.1134/s0031918x14120059

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The phenomenon of aging in the low-temperature nonequilibrium critical behavior of the two-dimensional XY model has been investigated by the Monte Carlo methods from different initial states. The temperature dependence of the transverse rigidity in the low-temperature critical behavior of the two-dimensional XY model has been investigated by the Monte Carlo methods.
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The Monte Carlo study of nonequilibrium memory effects in the two-dimensional pure and structurally disordered XY model in the low-temperature Berezinskii phase has been performed. Features of the correlation between memory and aging effects have been demonstrated. A qualitatively novel phenomenon for memory effects has been revealed: dynamic curves of the autocorrelation function in the thermal cycling time interval tend to the dynamic curves with the initial temperature. A unique implementation of memory effects has been demonstrated at both cooling and heating cycling of the system under the condition that cooling and heating temperatures are in the low-temperature Berezinskii phase. The influence of structural disorder on memory effects has been analyzed. It has been found that they are enhanced in the structurally disordered system owing to the enhancement of aging effects.
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.
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.
With a large-scale Monte Carlo simulation, the aging of the two-dimensional dynamic Ising and XY models is numerically studied. Starting from a disordered state, the systems are quenched to critical temperature Tc and then evolve according to dynamics of model A. By calculating the autocorrelation function A(t,t′) we observe the aging phenomenon for both spin systems. Then, relatively accurate values of the dynamic critical exponent λc and z are estimated. Especially, we confirm that for the two-dimensional XY model, there is a strong logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered.