Nonequilibrium Relaxation of Fluctuations of Physical Quantities

Ito, Nobuyasu; Hukushima, Koji; Ogawa, Keita; Ozeki, Yukiyasu

doi:10.1143/jpsj.69.1931

Cited by 71 publications

(61 citation statements)

References 31 publications

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“…The order parameter φ 6 starts to relax to the value of the equilibrium state. With this nonequilibrium relaxation (NER) behavior of order parameters, critical points and critical exponents of various phase transitions can be determined accurately [21,22,23,24]. This method is called a NER method.…”

Section: B Time Evolutionmentioning

confidence: 99%

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

2006

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We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bondorientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.

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Section: B Time Evolutionmentioning

confidence: 99%

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

2006

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“…[1][2][3][4][5][6][7][8][9][10][11] One may observe the relaxation of the order parameter (e.g., the magnetization in the ferromagnetic case) in the thermalization process from the complete ordered state. It provides the critical erature and the dynamic critical exponent accurately.…”

Section: §1 Introductionmentioning

confidence: 99%

“…It provides the critical erature and the dynamic critical exponent accurately. This analysis has been used successfully to study various such as ferromagnetic (FM) Ising dtemp problems mo 2808 els, [2][3][4][5] XY models, 6) spin glass models [7][8][9][10] and quantum spin systems. 11) Since only the process in equilibration is observed, one can simulate quite large systems; as large as the memory permits.…”

Section: §1 Introductionmentioning

confidence: 99%

“…Recently, the method is extended to estimate various exponents using quantities of fluctuations (susceptibility, specific heat and so on). 4,5) The critical exponents can be determined by asymptotic powers of such quantities or their combinations. The correlation length ξ(t) in the non-equilibrium process, which grows up to ξ eq , is finite transiently even at the critical point.…”

Section: §1 Introductionmentioning

confidence: 99%

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Non-Equilibrium Relaxation Study for Frustrated Spin System with Successive Phase Transitions

Ogawa

Ozeki

2000

J. Phys. Soc. Jpn.

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The frustrated system is one of main subjects in critical phenomena because of its rich phase diagrams and possibility of new universality classes. The equilibrium Monte Carlo simulation is a useful technique to study critical phenomena and has provided many helpful informations in statistical mechanics. Although it works even in frustrated systems, it sometimes suffers difficulties in the analysis due to large fluctuation and degeneracy, which restrict the available system sizes too small.In standard Monte Carlo simulations, the total amount of calculation time is consist of equilibration and averaging, and is, in usual, proportional to the equilibration time τ eq , since the averaging time is taken several times of τ eq . The equilibration from a fixed non-equilibrium state is achieved when the spin correlation ξ(t) grows up to the scale of the correlation length ξ eq in equilibrium or the system size L. In the critical regime, since ξ eq becomes larger than sizes simulated, τ eq becomes longer as L is larger. In frustrated systems, the fluctuation and degeneracy reveal a slow dynamics, that also makes τ eq very large. Therefore, available system sizes are reduced. In small systems, the correction to scaling is necessary to discuss critical phenomena accurately which makes estimations for the critical point and critical exponents complicated. The development and improvement of simulation technique in last decades have been mainly devoted to overcome such difficulties.Recently, efficient Monte Carlo technique is proposed to study critical phenomena using non-equilibrium relaxation (NER) process. 1-11) One may observe the relaxation of the order parameter (e.g., the magnetization in the ferromagnetic case) in the thermalization process from the complete ordered state. It provides the critical erature and the dynamic critical exponent accurately. This analysis has been used successfully to study various such as ferromagnetic (FM) Ising dtemp problems mo 2808 els, 2-5) XY models, 6) spin glass models 7-10) and quantum spin systems. 11) Since only the process in equilibration is observed, one can simulate quite large systems; as large as the memory permits. Recently, the method is extended to estimate various exponents using quantities of fluctuations (susceptibility, specific heat and so on). 4, 5)The critical exponents can be determined by asymptotic powers of such quantities or their combinations. The correlation length ξ(t) in the non-equilibrium process, which grows up to ξ eq , is finite transiently even at the critical point. The finite-size effect does not appear while ξ(t) L. If one may prepare systems with sizes larger than the maximum correlation length observed in the simulation, any finite-size effect is not necessary to be taken into account for the estimation of the critical point and the critical exponent. Therefore, the NER method is useful to study systems in which strong fluctuations appear or sufficient sizes can not be prepared on account of large equilibration time. It is appropriate much to st...

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“…Static critical exponents α/ν, β/ν and γ/ν are exact values for the d = 1 and d = 2 models [13,[28][29][30] and for d = 4 Ising [49], and are the best currently available numerical estimates for d = 3 Ising [41]. Exponent z G for Glauber dynamics is taken from [50, Table 1] for the d = 2 models (see also [51][52][53][54][55]), from [51,53,[56][57][58][59][60][61][62] for d = 3 Ising, and from [63] for d = 4 Ising. …”

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confidence: 99%

Dynamic critical behavior of the Swendsen?Wang algorithm for the three-dimensional Ising model

Ossola

2004

Nuclear Physics B

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We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find z int,N = z int,E = z int,E ′ = 0.459 ± 0.005 ± 0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find z int,M 2 = z int,S 2 = 0.443 ± 0.005 ± 0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find z exp ≈ 0.481. Our data are consistent with the Coddington-Baillie conjecture z SW = β/ν ≈ 0.5183, especially if it is interpreted as referring to z exp .

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Nonequilibrium Relaxation of Fluctuations of Physical Quantities

Cited by 71 publications

References 31 publications

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

Non-Equilibrium Relaxation Study for Frustrated Spin System with Successive Phase Transitions

Dynamic critical behavior of the Swendsen?Wang algorithm for the three-dimensional Ising model

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