Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder

Qin, Xing; Zheng, Bo; Zhou, N. J.

doi:10.1088/1751-8113/45/11/115001

Cited by 14 publications

(30 citation statements)

References 32 publications

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“…states of quiescence alternated with avalanches, before reaching the phase state of moving or pinning. Until today, theoretical approaches to explain the depinning transition of the MDW into disordered medium pushed by an external magnetic field, are based on: (a) the continuous equation of Edwards-Wilkinson with quenched noise (QEW) [29][30][31][32] and (b) discrete models based on microscopic structures and interactions, such as random-field Ising field model with driving (DRFIM) [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Intrinsic anomalous scaling in a ferromagnetic thin film model

Torres

Buceta

2013

Eur. Phys. J. B

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Recently, the interest on theoretical and experimental studies of dynamic properties of the magnetic domain wall (MDW) of ferromagnetic thin films with disorder placed in an external magnetic field has increased. In order to study global and local measurable observables, we consider the (1 + 1)-dimensional model introduced by Buceta and Muraca [Physica A 390 (2011) 4192], based on rules of evolution that describe the MDW avalanches. From the values of the roughness exponents, global ζ, local ζ loc , and spectral ζ s , obtained from the global interface width, hight-difference correlation function and structure function, respectively, recent works have concluded that the universality classes should be analyzed in the context of the anomalous scaling theory. We show that the model is included in the group of systems with intrinsic anomalous scaling (ζ ≃ 1.5, ζ loc = ζ s ≃ 0.5), and that the surface of the MDW is multi-affine. With these results, we hope to establish in short term the scaling relations that verify the critical exponents of the model, including the dynamic exponent z, the exponents of the distributions of avalanche-size τ and -duration α, among others.

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Section: Introductionmentioning

confidence: 99%

Intrinsic anomalous scaling in a ferromagnetic thin film model

Torres

Buceta

2013

Eur. Phys. J. B

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“…If the latter is correct and general, this would mean that critically pinned interfaces in 2-d isotropic media are always in the universality class of OP. This had been conjectured before [19], but the opposite was claimed in many, even very recent, papers [12][13][14][15][16][20][21][22][23][24][25][26][27] In most of these papers [12-16, 20, 26-28] it is claimed that the percolation scenario breaks down when the disorder is weak. But in others [23][24][25], even in the percolation like phase the critical exponents were found to be different.…”

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confidence: 99%

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

Grassberger

2018

Phys. Rev. Lett.

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Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

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“…S(k, t, ǫ = 0, L) is plotted against q for the pure case. Different curves correspond to exponentially increasing times (t = 2,3,5,7,11,18, 29, 46, 73, 118, 189, 304, 490, 789, 1269, 2044, 3291, 5299, 8532, 13739, 22123, 35623, 57362, 92368, 148736, 239503, 385663, 621017, 10 6 from bottom to top)…”

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confidence: 99%

Roughening of an interface in a system with surface or bulk disorder

Corberi

Lippiello²,

Zannetti

2016

J. Phys. A: Math. Theor.

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We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also away from it, in the bulk. The dynamical structure factor shows a rich crossover pattern from the form of a pure system at large wavevectors k, to a different behavior, typical of the kind of disorder, at smaller k's. For the random field model a second crossover is observed from the typical behavior of a system where disorder is only effective on the surface, as the random bond model, to the truly large scale behavior, where bulk-disorder is important, that is observed at the smallest wavevectors.

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Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder

Cited by 14 publications

References 32 publications

Intrinsic anomalous scaling in a ferromagnetic thin film model

Intrinsic anomalous scaling in a ferromagnetic thin film model

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

Roughening of an interface in a system with surface or bulk disorder

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