Depinning transition and thermal fluctuations in the random-field Ising model (original) (raw)
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Physical review, 2018
We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L × L × l which explain the size-driven critical crossover from two dimensions (l = const, L → ∞) to three dimensions (l ∝ L → ∞). A model of effective critical disorder R eff c (l,L) with a unique fitting parameter and no free parameters in the R eff c (l,L → ∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.
Numerical approach to metastable states in the zero-temperature random-field Ising model
Physical Review B, 2008
We study numerically the number of single-spin-flip stable states in the T = 0 Random Field Ising Model (RFIM) on random regular graphs of connectivity z = 2 and z = 4 and on the cubic lattice. The annealed and quenched complexities (i.e. the entropy densities) of the metastable states with given magnetization are calculated as a function of the external magnetic field. The results show that the appearance of a (disorder-induced) out-of-equilibrium phase transition in the magnetization hysteresis loop at low disorder can be ascribed to a change in the distribution of the metastable states in the field-magnetization plane.
Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics
Physical Review B, 2006
The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.
Diluted 3d-Random Field Ising Model at zero temperature with metastable dynamics
We study the influence of vacancy concentration on the behaviour of the three dimensional Random Field Ising model with metastable dynamics. We focus our analysis on the number of spanning avalanches which allows for a clean determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite size scaling analysis we determine the phase diagram and estimate numerically the critical exponents along the whole critical line. Finally we discuss the origin of the curvature of the critical line at high vacancy concentration.
The quenched-disordered Ising model in two and four dimensions
2009
We briefly review the Ising model with uncorrelated, quenched random-site or random-bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent α, which characterizes the specific-heat critical behaviour, vanishes and no Harris prediction for the consequences of quenched disorder can be made. In the two-dimensional case, the controversy is between the strong universality hypothesis which maintains that the leading critical exponents are the same as in the pure case and the weak universality hypothesis, which favours dilution-dependent leading critical exponents. Here the random-site version of the model is subject to a finite-size scaling analysis, paying special attention to the implications for multiplicative logarithmic corrections. The analysis is fully supportive of the scaling relations for logarithmic corrections and of the strong scaling hypothesis in the 2D case. In the four-dimensional case unusual corrections to scaling characterize the model, and the precise nature of these corrections has been debated. Progress made in determining the correct 4D scenario is outlined.
Glassy transition in the three-dimensional random-field Ising model
Physical Review B, 1994
The high temperature phase of the three dimensional random field Ising model is studied using replica symmetry breaking framework. It is found that, above the ferromagnetic transition temperature T f , there appears a glassy phase at intermediate temperatures T f < T < T b while the usual paramagnetic phase exists for T > T b only. Correlation length at T b is computed and found to be compatible with previous numerical results.
Critical aspects of the random-field Ising model
The European Physical Journal B, 2013
We investigate the critical behavior of the three-dimensional random-field Ising model (RFIM) with a Gaussian field distribution at zero temperature. By implementing a computational approach that maps the ground-state of the RFIM to the maximum-flow optimization problem of a network, we simulate large ensembles of disorder realizations of the model for a broad range of values of the disorder strength h and system sizes V = L 3 , with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 10 3 . Using well-established finitesize scaling schemes, the fourth-order's Binder cumulant, and the sample-to-sample fluctuations of various thermodynamic quantities, we provide high-accuracy estimates for the critical field hc, as well as the critical exponents ν, β/ν, andγ/ν of the correlation length, order parameter, and disconnected susceptibility, respectively. Moreover, using properly defined noise to signal ratios, we depict the variation of the self-averaging property of the model, by crossing the phase boundary into the ordered phase. Finally, we discuss the controversial issue of the specific heat based on a scaling analysis of the bond energy, providing evidence that its critical exponent α ≈ 0 − .
Phase transition in the 3d random field Ising model
Communications in Mathematical Physics, 1988
We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,d l for the theory isd l ≦2, settling a long controversy on the subject. Our proof is based on an exact Renormalization Group (RG) analysis of the system. This analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of Imry and Ma. The RG acts in the space of Ising models and in the space of random field distributions, driving the former to zero temperature and the latter to zero variance.
Coarsening and percolation in the Ising Model with quenched disorder
Journal of Physics: Conference Series, 2018
Through large-scale numerical simulations, we study the phase ordering kinetics of the 2d Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities-the winding angle and the pair-connectedness-we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.
Physical Review B, 1995
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length ξ diverges with an exponent ν = 1.1 ± 0.2 at the critical temperature and that χ ∼ ξ 2−η with η = 0.50 ± 0.05 for the connected susceptibility and χ dis ∼ ξ 4−η with η = 1.03 ± 0.05 for the disconnected susceptibility. Together with the amplitude ratio A = limT →Tc χ dis /χ 2 (hr/T) 2 being close to one this gives further support for a two exponent scaling scenario implying η = 2η. The magnetization behaves discontinuously at the transition, i.e. β = 0, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.