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Journal of Experimental and Theoretical Physics

Specific Features of the Effect of Structural Defects on the Correlation and Interaction of Vortex Excitations in the Nonequilibrium BKT Dynamics of the Two-Dimensional XY Model

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

Published Nov 1, 2020• 3 citations
Publisher

Abstract

Abstract A Monte Carlo simulation of the nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a high-temperature initial state. The features of the effect of structural disorder on the time dependence of the correlation length ξ(t) of the system and the dynamical scaling of the spin-spin autocorrelation function CSS(t, tw) are revealed. A direct calculation of the dynamic behavior of the correlation length ξ(t) of the two-dimensional structurally disordered XY model is carried out, and it is shown that this model, just as the pure model, exhibits a time dependence with a logarithmic correction ξ(t) ∝ (t/lnt)1/2, which is associated with the nonequilibrium annihilation of vortices and antivortices in the forming vortex pairs. Based on the analysis of the time dependence of the correlation length ξ(t) and the magnetization cumulant g2(t), it is shown that the two-dimensional XY model with the spin concentration p = 0.7 is so close to the spin percolation threshold pc that the influence of the attraction of the percolation fixed point becomes crucial for the relaxation properties of the system. However, the features of the critical dynamics of systems with spin concentrations of p = 0.9 and p = 0.8 are determined by the attraction of the pure fixed point. Temperature and concentration dependences of the Fisher critical exponent η(p, T) are determined using the scaling properties of the calculated two-time dependence of the spin-spin autocorrelation function CSS(t, tw). The scaling functions of the two-time dependence of the spin-spin autocorrelation function CSS(t, tw) are calculated using the dynamic dependence of the correlation length ξ(t) obtained as a result of simulation, and the values of the decay exponents λC(p, T) of the scaling functions in the long-time regime are determined, which are in good agreement with the relation λC(p, T) = 1 + η(p, T) and prove that the dynamical scaling is realized for the nonequilibrium characteristics of structurally disordered systems.

DOI
10.1134/s1063776120110096

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Abstract A Monte Carlo simulation of the nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a high-temperature initial state. The features of the effect of structural disorder on the time dependence of the correlation length ξ(t) of the system and the dynamical scaling of the spin-spin autocorrelation function CSS(t, tw) are revealed. A direct calculation of the dynamic behavior of the correlation length ξ(t) of the two-dimensional structurally disordered XY model is carried out, and it is shown that this model, just as the pure model, exhibits a time dependence with a logarithmic correction ξ(t) ∝ (t/lnt)1/2, which is associated with the nonequilibrium annihilation of vortices and antivortices in the forming vortex pairs. Based on the analysis of the time dependence of the correlation length ξ(t) and the magnetization cumulant g2(t), it is shown that the two-dimensional XY model with the spin concentration p = 0.7 is so close to the spin percolation threshold pc that the influence of the attraction of the percolation fixed point becomes crucial for the relaxation properties of the system. However, the features of the critical dynamics of systems with spin concentrations of p = 0.9 and p = 0.8 are determined by the attraction of the pure fixed point. Temperature and concentration dependences of the Fisher critical exponent η(p, T) are determined using the scaling properties of the calculated two-time dependence of the spin-spin autocorrelation function CSS(t, tw). The scaling functions of the two-time dependence of the spin-spin autocorrelation function CSS(t, tw) are calculated using the dynamic dependence of the correlation length ξ(t) obtained as a result of simulation, and the values of the decay exponents λC(p, T) of the scaling functions in the long-time regime are determined, which are in good agreement with the relation λC(p, T) = 1 + η(p, T) and prove that the dynamical scaling is realized for the nonequilibrium characteristics of structurally disordered systems.
Abstract The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.
The results of a numerical Monte Carlo study of features of defects influence on nonequilibrium critical behavior of the two-dimensional Ising model are presented. The logarithmic corrections for the correlation length of disordered systems with different spin concentrations are calculated. Analysis of correlation length time dependence and the two-time dependences of the autocorrelation function has revealed an influence of logarithmic corrections and crossover phenomena of percolation behavior on nonequilibrium characteristics and critical exponents.
Abstract The study of the effects of aging in the non-equilibrium critical relaxation of a two-dimensional XY-model with a non-equilibrium vortex annealing of structural disorder has been carried out. Two-time dynamic dependencies of the spin-spin and defect-defect autocorrelation functions C SS (t,t w) and C DD (t,t w) are obtained for the entire Berezinskii low-temperature phase T < T BKT(p), for a wide range of waiting times t w and spin concentrations p. Near the BKT phase transition point T BKT (p), the dynamic dependencies C DD(t,t w) become uniform with time. However, with a decrease in temperature in the low-temperature phase T < T BKT (p), this relaxation uniformity breaks down, and C DD(t,t w) does not exhibit canonical aging properties. The formation of a declining family of dynamical scaling curves is clearly observed at large observation times t – t w which may indicate the presence of an asymptotic scaling dependence of C DD (t, t w).
A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.
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.