Phase diagram of the 3D bimodal random-field Ising model

Fytas, Nikolaos G.; Malakis, A.

doi:10.1140/epjb/e2008-00039-7

Cited by 33 publications

(41 citation statements)

References 90 publications

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“…The phase-diagram line separates the two phases of the model and intersects the randomness axis at the critical value of the disorder strength. Such qualitative sketching has been commonly used in most papers for the RFIM [32][33][34][35][36][37] and closed form quantitative expressions are also known from the early mean-field calculations [37]. However, it is generally true that the quantitative aspects of phase diagrams produced by mean-field treatments are very poor approximations.…”

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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“…For higher temperatures, where the entropy dominates, or for higher random fields, where the spins are predominately aligned parallel to its local random fields, the system is paramagnetic. Such qualitative sketching has been commonly used for the RFIM [12][13][14] and closed form quantitative expressions are also known from the early mean-field calculations [15] and more recently from extensive Monte Carlo simulations [16].…”

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 situation has also been handled on three dimensional lattices with nearest-neighbor interactions by a variety of theoretical works such as EFT [57,58], EFT with multi site spin correlations [59], MC simulations [60][61][62], pair approximation [63], and the series expansion method [64].…”

Section: Introductionmentioning

confidence: 99%

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

Akıncı

2012

Journal of Magnetism and Magnetic Materials

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a b s t r a c tThe effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of Ising nanowire is investigated using effective field theory with correlations. Trimodal distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as reentrant behavior and first order transitions. Also for the trimodal distribution, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.

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Phase diagram of the 3D bimodal random-field Ising model

Cited by 33 publications

References 90 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

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

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