Kinetics of clusters in Ising models

Stauffer, Dietrich

doi:10.1016/0378-4371(92)90375-z

Cited by 90 publications

(77 citation statements)

References 34 publications

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“…Some evidences for the short-time dynamic scaling were also observed in Monte Carlo simulations [5][6][7]. Meanwhile, it was found that the power law decay of the magnetization starting from a completely ordered state emerges already in relatively early times, e.g., see [8], and it can be used to estimate the dynamic exponent z [9,10]. In recent years short-time critical dynamics has been systematically investigated with Monte Carlo simulations [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 96%

“…The values also coincide well with those obtained from dynamics of model A and measured in equilibrium for the standard Ising model. The static exponent ν for m s = 0.2 and 0.4 are 0.82 (8) and 0.81(3) respectively. Even though the first value carries a relatively big error, they are clearly different from ν = 0.64(2) for m s = 0.0 and those measured from dynamics of model A and in equilibrium.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

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Monte Carlo simulations of short-time critical dynamics with a conserved quantity

Zheng¹,

Luo²

2001

Phys. Rev. E

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With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional anti-ferromagnetic Ising model with a globally conserved magnetization m s (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the auto-correlation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of m s = 0 is the same as that without a conserved quantity, but the universality class of non-zero m s is different.

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Section: Introductionmentioning

confidence: 96%

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Monte Carlo simulations of short-time critical dynamics with a conserved quantity

Zheng¹,

Luo²

2001

Phys. Rev. E

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“…Similarly to Ω, this observable does not show a power-law behavior, "lagging" behind the magnetization for early simulation times. The early dynamic behavior in this case is already reasonably well fitted by an exponential approach to the equilibrium value (analogous to the one found for cluster numbers in [9]), thus depending on a relaxation time scale.…”

Section: Numerical Resultsmentioning

confidence: 79%

Dynamic behavior of cluster observables for the 2d Ising model

2006

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We present results of our numerical study of the critical dynamics of percolation observables for the twodimensional Ising model. We consider the (Monte Carlo) short-time evolution of the system with small initial magnetization and heat-bath dynamics. We find qualitatively different dynamic behaviors for the magnetization M and for Ω, the so-called strength of the percolating cluster, which is the order parameter of the percolation transition. More precisely, we obtain a (leading) exponential form for Ω as a function of the Monte Carlo time t, to be compared with the power-law increase encountered for M at short times. Our results suggest that, although the descriptions in terms of magnetic or percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times.

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“…Matsubara et al 15,16,17 showed several lines of evidence that the spin-glass transition occurs at a finite temperature. Nakamura et al 18,19 investigated the model by a nonequilibrium relaxation method 20,21,22,23,24 and obtained the consistent results. Here, we note that nonequilibrium relaxation of the spinglass susceptibility 25 and that of the Binder parameter 26 are known to exhibit the algebraic divergence at the spinglass transition temperature in the Ising model.…”

Section: Introductionmentioning

confidence: 87%

“…Kawamura and Li gave T cg = 0.39(3), ν κ = 1.2(2), γ κ /ν κ = 1.85 (20), and z κ = 7.4(10). Our estimation for the transition temperature is higher than their value.…”

Section: B Finite-time-scaling Analysesmentioning

confidence: 99%

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

2004

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A three-dimensional ±J XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider that the transition is driven by the spin degrees of freedom.

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Kinetics of clusters in Ising models

Cited by 90 publications

References 34 publications

Monte Carlo simulations of short-time critical dynamics with a conserved quantity

Monte Carlo simulations of short-time critical dynamics with a conserved quantity

Dynamic behavior of cluster observables for the 2d Ising model

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

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