Aging and non-equilibrium critical phenomena in Monte Carlo simulations of 3D pure and diluted Ising models

Прудников, П. В.; Прудников, В. В.; Pospelov, E. A.; Malyarenko, P. N.; Vakilov, A. N.

doi:10.1093/ptep/ptv055

Cited by 18 publications

(9 citation statements)

References 57 publications

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“…(6) and (7), it follows that the ratio of these times (8) should not depend on the linear size L of the lattice at T = T c . Thus, if we plot the characteristic curves for R(L, T) versus temperature at different values of L, Fig.…”

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confidence: 94%

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Damage spreading method in studies of the critical behavior of disordered systems

2015

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Theoretical and experimental studies of the critical behavior of disordered systems with quenched struc tural defects are of significant current interest. Most of the real solids contain quenched structural defects, which affect their characteristics and can appreciably modify the behavior characterizing phase transitions. This gives rise to novel complex phenomena in struc turally disordered systems. These phenomena are determined by the effects caused by anomalously strong interactions between fluctuations of some ther mal parameters. As a result, any perturbation intro duced by the structural defects even at their low den sity can lead to drastic changes in the state of the sys tem. The treatment of such systems demands developing special analytical and numerical tech niques.The analysis of the effect of the structural disorder on second order phase transitions leads to the follow ing two questions. First, do the critical exponents of a "pure" magnetic system change at the dilution of it by nonmagnetic impurities? Second, if they do change, are these new critical exponents universal, i.e., inde pendent of the density of structural effects up to the percolation threshold? The answer to the first question was given in [1]. It was shown that the critical expo nents for the systems with quenched structural defects differ from those characteristic of similar systems without defects if the critical exponent for the specific heat in the pure system is positive. This criterion is met only for three dimensional systems with the critical behavior described by the Ising model.The critical behavior of dilute Ising type magnetic systems was studied in [2-4] using the renormaliza tion group techniques, numerical Monte Carlo simu lations, and experimental methods. Currently, we have a positive answer to the question concerning the exist ence of the novel universality class for dilute Ising type magnetic systems. However, it is still not quite clear whether the asymptotic values of the critical expo nents are independent of the degree of dilution in the system, how the crossover effects can change these val ues, and whether two or more regimes of the critical behavior for weakly and strongly disordered systems can exist. These questions are still open and are actively discussed.In several studies of the critical dynamics in the dis ordered three dimensional Ising model with the use of both the renormalization group approach and numer ical simulations, it is shown that structural defects most clearly manifest themselves in the changes in the dynamic critical exponent z. This exponent character izes the anomalous growth (as compared to the changes in typical static critical exponents) of the relaxation rate in the system when it approaches the phase transition temperature. In this work, we use the damage spreading method to find out the effect of structural disorder on the dynamic critical behavior of the three dimensional Ising model with spin densities p = 0.6 and 0.8. This computer simulation technique is implemented as a to...

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confidence: 94%

“…For the numerical realization of evolution for spin systems, we use the Metropolis algorithm with one spin flip dynamics [8,9]. For the three dimen sional disordered Ising model with liner size L = 32 of the lattice at the time interval t = 500 Monte Carlo steps per second and at different temperature values ( Fig.…”

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confidence: 99%

Damage spreading method in studies of the critical behavior of disordered systems

2015

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“…It is well known that in the aging regime at t − t w ~ t w >> 1 the two-time autocorrelation function is characterized by the scaling form [4] ),…”

Section: Model Methods and Resultsmentioning

confidence: 99%

“…The nanoscale periodicity in magnetic multilayer structures gives rise to the mesoscopic effects of the spatial spin correlation with the slow relaxation dynamics of magnetization accompanying the quenching of the system in the non-equilibrium state. In contrast to the bulk magnetic systems, where the slow dynamics and aging effects manifest themselves near the critical point [4], magnetic superstructures with nanoscale periodicity allow increasing the relaxation time owing to the effects related to the larger characteristic spin-spin correlation length. That is why the aging and nonergodicity effects can be experimentally observed in the multilayer Co/Cr magnetic structure [5] within a wider temperature range as compared to that for the bulk magnetic systems.…”

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confidence: 99%

Monte Carlo simulation of aging phenomena in multilayer magnetic structures

et al. 2018

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A Monte Carlo simulation of the non-equilibrium behavior of multilayer magnetic structures consisting of alternating magnetic and nonmagnetic nanolayers is realized. The calculated two-time autocorrelation function for the structure during its evolution starting from high-temperature initial state is analyzed. The analysis reveals aging effects characterized by a slowing down of correlation characteristics in the system with increase of the waiting time. The dependence of aging characteristics on thickness of ferromagnetic films is investigated. It is shown that, in contrast to bulk magnetic systems, the aging effects in magnetic superstructures arise not only at the ferromagnetic ordering temperature Tc in the films but also within a wide temperature range at T ≤ Tc.

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“…It is well known that the two-time autocorrelation function is characterized in the aging regime at times t−t w ∼t w ? 1 by the scaling form [34] C t t t F t t , ,…”

Section: Simulation Of Equilibrium Properties Of the Multilayer Magnementioning

confidence: 99%

Manifestation of aging in giant magnetoresistance of the Co/Cu/Co nanostructure

Прудников

Mamonova

et al. 2019

J. Phys. Commun.

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A Monte Carlo simulation of the non-equilibrium behavior of multilayer magnetic nanostructure Co/Cu(100)/Co consisting of alternating magnetic and nonmagnetic nanolayers is carried out. Analysis of calculated two-time autocorrelation function for structure relaxing from both hightemperature and low-temperature initial states reveals aging characterized by a slowing down of correlation characteristics with increase of the waiting time. It is shown that, in contrast to bulk magnetic systems, the aging effects in nanostructure arise not only at the ferromagnetic ordering temperature T c but also within a wide temperature range at TT c . For evolution from hightemperature initial state, the study of dependence of aging characteristics on thickness N of cobalt films reveals a weakening of the aging with increasing N at the critical temperatures T c (N) and an opposite tendency at temperatures T<T c (N) with strengthening of aging with increasing N for considered N9 ML. This phenomenon is connected with increasing correlation and relaxation times in nanostructures when temperature is decreased. For case of the low-temperature initial state, it is shown that correlation times are two-three orders of magnitude smaller than those in the evolution from a high-temperature initial state at the same t w values. In this case, time behavior of the autocorrelation function doesn't depend considerably on temperature for T s T c and thickness N of cobalt films. Simulation of transport properties in Co/Cu(100)/Co structure permitted to calculate temperature dependence of its equilibrium magnetoresistance values. For the first time, it was revealed influence of non-equilibrium behavior on the magnetoresistance with demonstration of nontrivial aging effects. It has been shown that the magnetoresistance reaches plateau in asymptotic long-time regime with values N T , d ¥ ( ), which depend on type of initial state, thickness of cobalt films, and temperature.

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Aging and non-equilibrium critical phenomena in Monte Carlo simulations of 3D pure and diluted Ising models

Cited by 18 publications

References 57 publications

Damage spreading method in studies of the critical behavior of disordered systems

Damage spreading method in studies of the critical behavior of disordered systems

Monte Carlo simulation of aging phenomena in multilayer magnetic structures

Manifestation of aging in giant magnetoresistance of the Co/Cu/Co nanostructure

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