Dynamic exponent of the 3D Ising spin glass

Blundell, R.; Humayun, K; Bray, A. J.

doi:10.1088/0305-4470/25/12/005

Cited by 41 publications

(43 citation statements)

References 10 publications

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“…Aging is just a kind of scaling or quasiscaling. Dynamic scaling behavior around a spin glass transition [5,[37][38][39]21] is very similar to that around a standard critical point. For example, the experimental measurements of the remanent magnetization in spin glasses support not only the power law scaling behavior but also the scaling relations between the exponents [40,21].…”

Section: Introductionmentioning

confidence: 68%

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: 68%

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

Zheng¹,

Luo²

2001

Phys. Rev. E

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“…This provides us with a direct method for estimating z(T ). Alternative techniques which have been used for estimating the value of z(T ) independently of the other exponents are the monitoring of the time variation of the Binder parameter for different sample sizes 29 or the scaling of the time-dependent spin-glass susceptibility χ(L, t) for different sizes L 6 . The present method is more convenient than the Binder parameter measurements as the latter are intrinsically noisy.…”

Section: Out Of Equilibrium Methodsmentioning

confidence: 99%

Critical properties of the three- and four-dimensional gauge glass

Katzgraber

Campbell²

2004

Phys. Rev. B

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The gauge glass in dimensions 3 and 4 is studied using a variety of numerical methods, in order to obtain accurate and reliable values for the critical parameters. Detailed comparisons are made of the sensitivity of the different techniques to corrections to finite-size scaling, which are generally the major source of systematic error in such measurements. For completeness we also present results in two dimensions. The variation of the critical exponents with space dimension is compared to results in Ising spin glasses.Comment: 19 pages, 27 figures, 6 table

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“…Both uniform (all spins parallel) and disordered (randomly orientated spins) initial conditions were employed. In both cases, the 'time-dependent Binder cumulant' [21,22] …”

Section: Comparison With Simulation Datamentioning

confidence: 99%

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensionalXYmodel

Bray

2000

Phys. Rev. E

132

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The Langevin equation for a particle ('random walker') moving in d-dimensional space under an attractive central force and driven by a Gaussian white noise is considered for the case of a power-law force, F (r) ∼ −r −σ . The 'persistence probability', P0(t), that the particle has not visited the origin up to time t, is calculated for a number of cases. For σ > 1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P0(t) are those of a free random walker. For σ < 1, the noise is (dangerously) irrelevant and the asymptotics of P0(t) can be extracted from a weak noise limit within a path-integral formalism employing the Onsager-Machlup functional.The case σ = 1, corresponding to a logarithmic potential, is most interesting because the noise is exactly marginal. In this case, P0(t) decays as a power-law, P0(t) ∼ t −θ with an exponent θ that depends continuously on the ratio of the strength of the potential to the strength of the noise. This case, with d = 2, is relevant to the annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY model. Although the noise is multiplicative in the latter case, the relevant Langevin equation can be transformed to the standard form discussed in the first part of the paper. The mean annihilation time for a pair initially separated by r is given by t(r) ∼ r 2 ln(r/a) where a is a microscopic cut-off (the vortex core size). Implications for the nonequilibrium critical dynamics of the system are discussed and compared to numerical simulation results.

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Dynamic exponent of the 3D Ising spin glass

Cited by 41 publications

References 10 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

Critical properties of the three- and four-dimensional gauge glass

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensionalXYmodel

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