Critical aspects of the random-field Ising model

Nikolaos G. Fytas, Panagiotis E. Theodorakis, Ioannis Georgiou, Ioannis Lelidis

    Research output: Contribution to journalArticle

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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 �� = L 3, with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 103. Using well-established finite-size 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 h c, as well as the critical exponents ν, β/ν, and γ̅/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−.
    Original languageEnglish
    Article number268
    JournalThe European Physical Journal B
    Volume86
    Issue number6
    DOIs
    Publication statusPublished - Jun 2013

    Fingerprint

    Ising model
    Ground state
    exponents
    disorders
    scaling
    ground state
    Phase boundaries
    Specific heat
    Binders
    Signal to noise ratio
    signal to noise ratios
    sampling
    specific heat
    Thermodynamics
    Sampling
    magnetic permeability
    thermodynamics
    optimization
    estimates
    Temperature

    Keywords

    • Ground state
    • Computational approach
    • Correlation lengths
    • Finite size scaling
    • Noise-to-signal ratios
    • Optimization problems
    • Random field Ising models
    • Sample-to-sample fluctuations
    • Thermodynamic quantities

    Cite this

    Critical aspects of the random-field Ising model. / Fytas, Nikolaos G.; Theodorakis, Panagiotis E.; Georgiou, Ioannis; Lelidis, Ioannis.

    In: The European Physical Journal B, Vol. 86, No. 6, 268, 06.2013.

    Research output: Contribution to journalArticle

    Fytas, Nikolaos G. ; Theodorakis, Panagiotis E. ; Georgiou, Ioannis ; Lelidis, Ioannis. / Critical aspects of the random-field Ising model. In: The European Physical Journal B. 2013 ; Vol. 86, No. 6.
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    KW - Sample-to-sample fluctuations

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