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arXiv:1601.00277 · Computer Physics Communications

Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models

Lisha Si, Xiaoyun Liao, Nengji Zhou

Published Aug 22, 2016• 10 citations
arXivHTMLPDF
DOI
10.1016/j.cpc.2016.08.009

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With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equation but agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.
Abstract Large‐scale Monte Carlo simulations, based on the invariance of the Binder cumulant Q, for continuous phase transitions in the three‐dimensional Ashkin–Teller spin‐lattice model on a cubic lattice, have been performed. Using the universality hypotesis and the finite‐size‐scaling analysis, the Ising character of phase transitions from the antiferro‐ to paramagnetic phase, where the cumulant Q behavior is different than in the Ising model, is demonstrated. Some preliminary results demonstrating the existance of the tricritical points are also presented.
With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence of the updating schemes of the Monte Carlo algorithm. From the roughness exponents ζ, ζ loc and ζ s , one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with ζ ≠ ζ loc ≠ ζ s and ζ loc ≠ 1. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution.