Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of the Solid State

Монте-Карло-исследование влияния начальных состояний и дефектов структуры на неравновесное критическое поведение трехмерной модели Изинга

В.В. Прудников, П.В. Прудников, P. N. Malyarenko

Published Jan 1, 2018• 0 citations
Publisher

Abstract

AbstractThe effect of various initial magnetizations m _0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m _0 These subclasses correspond to the system evolution from the high-temperature ( m _0 = 0) and low-temperature ( m _0 = 1) initial states with limit FDRs characteristic of these states.

DOI
10.21883/ftt.2018.06.45981.05m

Related papers

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, P. N. Malyarenko

The effect of various initial magnetizations m0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m0 These subclasses correspond to the system evolution from the high-temperature (m0 = 0) and low-temperature (m0 = 1) initial states with limit FDRs characteristic of these states.

Physics of the Solid State•Jun 1, 2018•2 citations

Исследование влияния начальных состояний, анизотропии и дефектов структуры на неравновесное критическое поведение трехмерной модели Гейзенберга

В.В. Прудников, П.В. Прудников, Лях Анастасия Сергеевна

A numerical Monte Carlo study of different initial states, magnetic anisotropy of “easy axis” type, and structural defects influence on non-equilibrium critical behavior of the classical three-dimensional Heisenberg model has been carried out. Analysis of time dependence of the magnetization and the autocorrelation function for isotropic Heisenberg model has shown strong influence of initial states on relaxation of the magnetization and aging effects in behavior of the autocorrelation function, which are characterized by anomalous slowing down of relaxation and correlation in system with increasing waiting time. Study of the anisotropic Heisenberg model with magnetic anisotropy of “easy axis” type has revealed that behavior of the magnetization and autocorrelation function in long-time regime is characterized by critical exponents of the three-dimensional Ising model and more fast decay of the autocorrelation function than for isotropic Heisenberg model. It has been revealed that in structurally disordered isotropic Heisenberg model relaxing from the low-temperature initial state, the significant changes of non-equilibrium aging phenomena in comparison with pure model are observed due to the pinning of domain walls on defects. It has been shown that during this relaxation process a strong slowing-down of time dependence of the autocorrelation function is realized. As a result, superaging effects occur in long-term behavior of the autocorrelation function with values of the superaging exponent μ=2.6(1). During evolution of system from high-temperature initial state, the presence of structural defects leads to increase of aging effects in aging regime, but their influence is found irrelevant in long-time regime.

Physics of the Solid State•Jan 1, 2020•0 citations

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, P. N. Malyarenko +1 more

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.

Journal of Experimental and Theoretical Physics•Feb 1, 2020•3 citations

Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

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

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.

Journal of Experimental and Theoretical Physics•Mar 1, 2018•11 citations

Исследование неравновесной критической эволюции структурно неупорядоченной трехмерной модели Изинга

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Evgenii A. Pospelov +2 more

Using Monte Carlo simulations it was studied the non-equilibrium critical evolution in the three-dimensional site-diluted weakly and strongly disordered Ising model with spin concentrations p=0.80 and 0.60. The values of exponents for power-law time dependence of magnetization and the autocorrelation function were determined. The values of two independent dynamic critical exponents z and θ were calculated. They demonstrate a good agreement with results of theoretical-field description and results of experimental investigations for weakly diluted Ising-like systems, but show visible differences with values of these exponents for strongly disordered Ising systems.

Herald of Omsk University Series Psychology•Jan 1, 2008•0 citations

Effect of the Initial States, the Anisotropy, and Structural Defects on a Nonequilibrium Critical Behavior of the Three-Dimensional Heisenberg Model

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Лях Анастасия Сергеевна

Abstract A numerical Monte Carlo study has been performed on the influence of various initial states, easy-axis-type magnetic anisotropy, and structural defects on a nonequilibrium critical behavior of the classical three-dimensional Heisenberg model. An analysis of the time dependence of the magnetization and the autocorrelation function for the isotropic Heisenberg model shows substantial influence of the initial states on the relaxation of the magnetization and the aging effects in the behavior of the autocorrelation function, which are characterized by anomalous slowing down of the relaxation and correlation in the system as the waiting time increases. The study of the anisotropic Heisenberg model shows that the behavior of the magnetization and the autocorrelation function in a long-time regime is characterized by the critical exponents of the three-dimensional Ising model with a faster time decay of the autocorrelation function than that for the isotropic model. It has been revealed that the existence of structural defects in the case of the evolution of the system from the low-temperature initial state leads to an anomalously significant slowing down of the autocorrelation function. These features in the behavior of the autocorrelation function are characterized by the “superaging” effect with “superaging” exponent μ = 2.6(1) and related to the pinning of domain walls on structural defects during a nonequilibrium change in the domain structure of the system. In the case of evolution from the high-temperature initial state, the structural defects enhance the aging effect in the aging regime but their influence is irrelevant in the long-time regime.

Physics of the Solid State•May 1, 2020•1 citation
AbstractThe effect of various initial magnetizations m _0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m _0 These subclasses correspond to the system evolution from the high-temperature ( m _0 = 0) and low-temperature ( m _0 = 1) initial states with limit FDRs characteristic of these states.
The effect of various initial magnetizations m0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m0 These subclasses correspond to the system evolution from the high-temperature (m0 = 0) and low-temperature (m0 = 1) initial states with limit FDRs characteristic of these states.
A numerical Monte Carlo study of different initial states, magnetic anisotropy of “easy axis” type, and structural defects influence on non-equilibrium critical behavior of the classical three-dimensional Heisenberg model has been carried out. Analysis of time dependence of the magnetization and the autocorrelation function for isotropic Heisenberg model has shown strong influence of initial states on relaxation of the magnetization and aging effects in behavior of the autocorrelation function, which are characterized by anomalous slowing down of relaxation and correlation in system with increasing waiting time. Study of the anisotropic Heisenberg model with magnetic anisotropy of “easy axis” type has revealed that behavior of the magnetization and autocorrelation function in long-time regime is characterized by critical exponents of the three-dimensional Ising model and more fast decay of the autocorrelation function than for isotropic Heisenberg model. It has been revealed that in structurally disordered isotropic Heisenberg model relaxing from the low-temperature initial state, the significant changes of non-equilibrium aging phenomena in comparison with pure model are observed due to the pinning of domain walls on defects. It has been shown that during this relaxation process a strong slowing-down of time dependence of the autocorrelation function is realized. As a result, superaging effects occur in long-term behavior of the autocorrelation function with values of the superaging exponent μ=2.6(1). During evolution of system from high-temperature initial state, the presence of structural defects leads to increase of aging effects in aging regime, but their influence is found irrelevant in long-time regime.
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.
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.
Using Monte Carlo simulations it was studied the non-equilibrium critical evolution in the three-dimensional site-diluted weakly and strongly disordered Ising model with spin concentrations p=0.80 and 0.60. The values of exponents for power-law time dependence of magnetization and the autocorrelation function were determined. The values of two independent dynamic critical exponents z and θ were calculated. They demonstrate a good agreement with results of theoretical-field description and results of experimental investigations for weakly diluted Ising-like systems, but show visible differences with values of these exponents for strongly disordered Ising systems.
Abstract A numerical Monte Carlo study has been performed on the influence of various initial states, easy-axis-type magnetic anisotropy, and structural defects on a nonequilibrium critical behavior of the classical three-dimensional Heisenberg model. An analysis of the time dependence of the magnetization and the autocorrelation function for the isotropic Heisenberg model shows substantial influence of the initial states on the relaxation of the magnetization and the aging effects in the behavior of the autocorrelation function, which are characterized by anomalous slowing down of the relaxation and correlation in the system as the waiting time increases. The study of the anisotropic Heisenberg model shows that the behavior of the magnetization and the autocorrelation function in a long-time regime is characterized by the critical exponents of the three-dimensional Ising model with a faster time decay of the autocorrelation function than that for the isotropic model. It has been revealed that the existence of structural defects in the case of the evolution of the system from the low-temperature initial state leads to an anomalously significant slowing down of the autocorrelation function. These features in the behavior of the autocorrelation function are characterized by the “superaging” effect with “superaging” exponent μ = 2.6(1) and related to the pinning of domain walls on structural defects during a nonequilibrium change in the domain structure of the system. In the case of evolution from the high-temperature initial state, the structural defects enhance the aging effect in the aging regime but their influence is irrelevant in the long-time regime.