Short-time critical dynamics of the two-dimensional random-bond Ising model

Luo, H. J.; Schülke, L.; Zheng, Bo

doi:10.1103/physreve.64.036123

Cited by 23 publications

(24 citation statements)

References 34 publications

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“…The derivation of the effective action for site dilution in the N = 0 Gross-Neveu form (9) thus supports the idea of the double-logarithmic singularity in specific heat and only logarithmic corrections to the pure-case power laws in other functions (as in the DD-SSL scheme) also for random-site 2D Ising ferromagnets, for weak quenched dilution [14]. For more details and a recent discussion of the effects of quenched disorder in RB and RS versions of 2DIM along theoretical and experimental (Monte-Carlo) lines also see [19,22,23,24,25,26,27,28,29,30,31]. In conclusion, we note that the fermionic integrals like ( 5), ( 6) and ( 8) are still the exact lattice expressions for Z (either its reduced version Q).…”

Section: Introductionsupporting

confidence: 67%

Fermions and disorder in ising and related models in two dimensions

Plechko¹

2010

Phys. Part. Nuclei

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Section: Introductionsupporting

confidence: 67%

Fermions and disorder in ising and related models in two dimensions

Plechko¹

2010

Phys. Part. Nuclei

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“…6 can be thus possibly ascribed to leading-order power-law scaling corrections to the universal nonsteady dynamics, similar to what is observed in the Ising, Potts, and XY models for instance [57][58][59]. As is customary, one can try here to fit a "corrected" formula in order to get an unbiased value for β/νz:…”

Section: Robustness Of the Crossoversmentioning

confidence: 99%

Nonsteady relaxation and critical exponents at the depinning transition

2013

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We study the nonsteady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units. We compute the timedependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, nonuniversal microscopic time regime, we find a nontrivial long crossover towards the nonsteady macroscopic critical regime. This "mesoscopic" time regime is robust under changes of the microscopic disorder, including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms, yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L 2 25 ) simulations for the nonsteady dynamics of the continuum displacement quenched Edwards-Wilkinson equation, getting accurate and consistent depinning exponents for this class: β = 0.245 ± 0.006, z = 1.433 ± 0.007, ζ = 1.250 ± 0.005, and ν = 1.333 ± 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent β) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

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“…The critical exponents θ and θ ′ depend on the dynamic universality class [17] and have been calculated by the RG method for a number of dynamic models [18] such as the model with a non-conserved order parameter [16,19] (model A), the model with an order parameter coupled to a conserved density [20] (model C), and the models with reversible mode coupling [21] (models E, F, G, and J). The universal scaling behavior of the initial stage of the critical relaxation for pure systems has been verified by extensive numerical simulations [22][23][24][25]. The developed method in these papers of short-time critical dynamics gives the possibility to determine both the static critical exponents ν, β, and dynamic critical exponents z and θ ′ in the macroscopic short-time regime of the critical relaxation.…”

Section: Introductionmentioning

confidence: 82%

Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

Прудников

Krinitsyn

et al. 2010

Phys. Rev. E

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Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

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Short-time critical dynamics of the two-dimensional random-bond Ising model

Cited by 23 publications

References 34 publications

Fermions and disorder in ising and related models in two dimensions

Fermions and disorder in ising and related models in two dimensions

Nonsteady relaxation and critical exponents at the depinning transition

Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

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