Field distributions and tricritical points in a random-field Ising model: Mean-field renormalization-group approach

Arruda, A.S. de; Figueiredo, W.; Sebastianes, R. M.; Saxena, Vishal

doi:10.1103/physrevb.39.4409

Cited by 26 publications

(14 citation statements)

References 22 publications

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“…The criteria for determining the order of the low temperature phase transition and its dependence on the form of the field distribution have been discussed throughout the years [37,[67][68][69][70][71][72][73]. In fact, different results have been proposed for different field distributions, like the existence of a tricritical point at the strong disorder regime of the system, present only in the bimodal distribution [37,69].…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

Fytas

Martı́n-Mayor²

2016

Phys. Rev. E

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It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

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Section: Introductionmentioning

confidence: 99%

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

Fytas

Martı́n-Mayor²

2016

Phys. Rev. E

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“…This in turn indicated that the two models should be in the same universality class. Further studies along these lines, using meanfield and renormalization-group approaches, provided contradicting evidence for the critical aspects of the p = 1/3 model and also proposed several approximations of its phase diagram for a range of values of p [40][41][42]. Only very recently accurate numerical data at zero temperature have been presented at d = 3, indicating that the original suggestion of Mattis is most probably correct [43].…”

Section: Introductionmentioning

confidence: 99%

Universality in four-dimensional random-field magnets

Fytas

Theodorakis

2015

Eur. Phys. J. B

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Abstract. We investigate the universality aspects of the four-dimensional random-field Ising model (RFIM) using numerical simulations at zero temperature. We consider two different, in terms of the field distribution, versions of the model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and system sizes. Using as finite-size measures the sample-to-sample fluctuations of the order parameter of the system, we propose, for both types of distributions, estimates of the critical field hc and the critical exponent ν of the correlation length, the latter suggesting that the two models in four dimensions share the same universality class. PACS

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“…The criteria for determining the order of the phase transition and its dependence on the field distribution have been discussed throughout the years [15][16][17][18][19][20][21][22][23][24][25][26]. In fact, different results have been proposed for different field distributions, like the existence of a tricritical point at the strong disorder regime of the system, present only in the bimodal case [15][16][17]20].…”

Section: Introductionmentioning

confidence: 99%

Critical aspects of the random-field Ising model

et al. 2013

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Abstract.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 − .

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Field distributions and tricritical points in a random-field Ising model: Mean-field renormalization-group approach

Cited by 26 publications

References 22 publications

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

Universality in four-dimensional random-field magnets

Critical aspects of the random-field Ising model

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