Computer simulation of the critical behavior of 3D disordered ising model

Прудников, В. В.; Прудников, П. В.; Vakilov, A. N.; Krinitsyn, Aleksandr

doi:10.1134/s1063776107080092

Cited by 38 publications

(30 citation statements)

References 18 publications

(27 reference statements)

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“…(iii) We have no evidence of two different universality classes depending on the disorder strength [44,45]. In particular, we show that the critical behavior is not influenced by the geometrical structure of the vacancies and does not depend whether the vacancies percolate or not.…”

Section: Discussionmentioning

confidence: 63%

Relaxational dynamics in 3D randomly diluted Ising models

Hasenbusch

Pelissetto²,

Vicari

2007

J. Stat. Mech.

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Abstract.We study the purely relaxational dynamics (model A) at criticality in threedimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bonddiluted Ising models, and the ±J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z = 2.35(2) for the universal dynamic critical exponent. We also study the offequilibrium relaxational dynamics following a quench from T = ∞ to T = T c . In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z = 2.35(2).Relaxational dynamics in 3D randomly diluted Ising models 2

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Section: Discussionmentioning

confidence: 63%

Relaxational dynamics in 3D randomly diluted Ising models

Hasenbusch

Pelissetto²,

Vicari

2007

J. Stat. Mech.

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“…Metropolis's algorithm, which consists of choosing randomly the spin S i , and flipping the spin with probability determined by the function W in Eq. [17] in the units J/k. We have used here the Monte Carlo method combined with the dynamical renormalization group method [22], to determine the dynamic exponent z characterizing the critical increase in the relaxation time of the system t rel ∼ |T − T c | −zν .…”

Section: Description Of the Model And Methodsmentioning

confidence: 99%

“…However, it remains unclear whether the asymptotic values of critical exponents are independent of the rate of dilution of the system, how the crossover effects change these values, and whether two or more regimes of the critical behavior exist for weakly and strongly disordered systems. These questions are the subjects of heated discussions [2,15] and extensive Monte Carlo simulations for site-diluted [16][17][18] and bond-diluted [19,20] three-dimensional Ising models.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo renormalization group of dilute 3D Ising dynamics

Прудников

Vakilov

Zolotarev

2014

J. Phys.: Conf. Ser.

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“…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][3][4][5][6][7][8][9] using the renormalization-group techniques, numerical Monte Carlo simulations, and experimental methods. Currently, we have a positive answer to the question concerning the existence of the novel universality class for dilute Ising-type magnetic systems.…”

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confidence: 99%

Zeros in Partition Function and Critical Behavior of Disordered Three Dimensional Ising Model

Vakilov¹

2017

J. Sib. Fed. Univ., Math. phys.

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The analysis of the effect of the structural disorder on second order phase transitions leads to the following 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., independent of the concentration of structural effects up to the percolation threshold? The answer to the first question was given in [1]. It was shown that the critical exponents 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 [2-9] using the renormalization-group techniques, numerical Monte Carlo simulations, and experimental methods. Currently, we have a positive answer to the question concerning the existence 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 exponents are independent of the degree of dilution in the system, how the crossover effects can change these values, 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.

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Computer simulation of the critical behavior of 3D disordered ising model

Cited by 38 publications

References 18 publications

Relaxational dynamics in 3D randomly diluted Ising models

Relaxational dynamics in 3D randomly diluted Ising models

Monte Carlo renormalization group of dilute 3D Ising dynamics

Zeros in Partition Function and Critical Behavior of Disordered Three Dimensional Ising Model

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