Dynamic scaling of disordered Ising systems

Heuer, H.-O.

doi:10.1088/0305-4470/26/6/008

Cited by 39 publications

(33 citation statements)

References 25 publications

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“…Previous MC studies [18,19,20,21,22,23] of equilibrium and off-equilibrium dynamics apparently have not confirmed the FT general predictions. They have mainly focused on the dynamic critical exponent z, which characterizes the divergence of the autocorrelation times when approaching the critical point.…”

Section: Introductionmentioning

confidence: 85%

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: Introductionmentioning

confidence: 85%

Relaxational dynamics in 3D randomly diluted Ising models

Hasenbusch

Pelissetto²,

Vicari

2007

J. Stat. Mech.

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“…It is clear that a more precise experiment on this issue will be welcome. We should point out that the critical dynamics of a diluted antiferromagnet is the same as of a diluted ferromagnet.A numerical study of the on-equilibrium dynamics in diluted systems was performed in 1993 by Heuer [9]. He measured the equilibrium autocorrelation functions for different concentrations and lattice sizes.…”

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confidence: 99%

“…A numerical study of the on-equilibrium dynamics in diluted systems was performed in 1993 by Heuer [9]. He measured the equilibrium autocorrelation functions for different concentrations and lattice sizes.…”

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confidence: 99%

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Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

1999

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We study the off-equilibrium critical dynamics of the three dimensional diluted Ising model. We compute the dynamical critical exponent z and we show that it is independent of the dilution only when we take into account the scaling-corrections to the dynamics. Finally we will compare our results with the experimental data.PACS numbers: 05.50.+q, 75.10.Nr, 75.40.Mg The issue of Universality in disordered systems is a controversial and interesting subject.Very often in the past it has been argued that critical exponents change with the strength of the disorder [1]. While, on a deeper analysis, it has turned out that those exponents were "effective" ones, i.e. they are affected by strong scaling corrections. So, when one studies the critical behavior of a disordered system it is mandatory to control the leading correction-to-scaling in order to avoid these effects that could modify the dilution-independent values of the critical exponents. For instance, in Ref.[2] the equilibrium critical behavior of the three dimensional diluted Ising model was studied. The authors showed that taking into account the corrections-to-scaling it was possible to show that the static critical exponents (e.g. ν and η) and cumulants were dilution-independent. These numerical facts supports the (static) perturbative renormalization group picture: all the points of the critical line (with p < 1) belong to the same Universality class (with critical exponents given by the random fixed point) [3]. Their final values of the exponents [2] were in very good agreement with the experimental figures (see below).We will show that an analogous effect also happens in the off-equilibrium dynamics of the diluted ferromagnetic model and we will take it into account in our data analysis, in order to get the best estimate of the critical dynamical exponent.The critical dynamics of the diluted Ising model has been studied experimentally in Ref.[4] using neutron spin-echo inelastic scattering on samples of Fe 0.46 Zn 0.54 F 2 (antiferromagnetic diluted model) and has been compared with the results obtained in pure samples (FeF 2 ) [4]. For the pure model a dynamical critical exponent z = 2.1(1) was found (in good agreement with the theoretical predictions based on one-loop perturbative renormalization group (PRG) [5]) whereas in the diluted case the exponent z = 1.7(2) was computed (three standard deviations away of the analytical prediction based on (one-loop) PRG that provides z ≃ 2.34 [6]). Furthermore, the dynamical exponent was computed in the framework of the PRG up to two loops and it was obtained z = 2.237 [7] and z = 2.180 [8] (the experimental value is at 2.5 standard deviation of the two loops analytical result).In the experiment [4] were measured critical amplitudes 100 times smaller than those computed in the pure case. It is clear that a more precise experiment on this issue will be welcome. We should point out that the critical dynamics of a diluted antiferromagnet is the same as of a diluted ferromagnet.A numerical study of the on-equilibr...

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“…Проведем теперь сопоставление рассчитанных в данной работе значений динами-ческого критического индекса для неупорядоченных систем с результатами компью-терного моделирования критической динамики неупорядоченной трехмерной мо- [32]. Данные результаты моделирования критической динамики находятся в достаточно хорошем согласии с результатами теоретико-полевого расчета с использованием методов суммирования лишь для сла-бо неупорядоченных систем с p 0.8, в то время как для сильно неупорядоченных систем наблюдается заметное расхождение результатов.…”

Section: заключениеunclassified

Расчет Динамического Критического Индекса Методом Суммирования Асимптотических Рядов

Krinitsyn¹,

Прудников²,

Прудников³

2006

ТМФ

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РАСЧЕТ ДИНАМИЧЕСКОГО КРИТИЧЕСКОГО ИНДЕКСА МЕТОДОМ СУММИРОВАНИЯ АСИМПТОТИЧЕСКИХ РЯДОВРассмотрено применение методов суммирования асимптотических рядов Паде-Бореля, Паде-Бореля-Лероя и конформного отображения к расчету ди-намического критического индекса для однородных и неупорядоченных изин-гоподобных систем.Ключевые слова: методы суммирования, асимптотические ряды, критическая дина-мика, ренормализационная группа, динамический критический индекс. ВВЕДЕНИЕДанная работа посвящена изложению деталей применения методов суммирова-ния асимптотических рядов для расчета критического индекса z, определяющего критическое замедление времени релаксации системы τ ∼ ξ z ∼ |T − T c | −zν вбли-зи температуры T c фазового перехода второго рода (ξ -корреляционная длина, ν -индекс корреляционной длины). Наиболее сложным и интересным направлени-ем теории критических явлений является исследование динамических процессов в окрестности критической точки. Существенным достижением ренормализационно-группового (РГ) подхода в исследовании статических критических явлений явилось создание концепции классов универсальности критического поведения различных систем, характеризующихся сходными критическими свойствами. Универсальность динамических критических явлений в отличие от статических значительно слабее, что проявляется в существовании большого числа моделей критической динамики с различным динамическим критическим поведением [1] при общих равновесных кри-тических свойствах. Эта трудность частично компенсируется тем, что динамические критические характеристики многих из этих моделей могут быть выражены через характеристики их статического критического поведения. В первую очередь это ка-сается моделей, в которых выполняются законы сохранения параметра порядка или * Омский государственный университет, Омск, Россия.

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Dynamic scaling of disordered Ising systems

Cited by 39 publications

References 25 publications

Relaxational dynamics in 3D randomly diluted Ising models

Relaxational dynamics in 3D randomly diluted Ising models

Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

Расчет Динамического Критического Индекса Методом Суммирования Асимптотических Рядов

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