Critical aspects of the random-field Ising model

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

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    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
    Issue number6
    Publication statusPublished - Jun 2013


    Georgiou acknowledges financial support by Marie Curie ITN-COMPLOIDS (Grant Agreement No. 234810).


    • 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


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