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Critical aspects of the random-field Ising model

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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 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−.

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Authors and Affiliations

  1. Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK

    Nikolaos G. Fytas

  2. Department of Physics, University of Athens, Panepistimiopolis, 15784 Zografos, Athens, Greece

    Nikolaos G. Fytas & Ioannis Lelidis

  3. Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK

    Panagiotis E. Theodorakis

  4. Institute for Theoretical Physics and Center for Computational Materials Science, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Ioannis Georgiou

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  1. Nikolaos G. Fytas
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  2. Panagiotis E. Theodorakis
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  3. Ioannis Georgiou
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  4. Ioannis Lelidis
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Correspondence to Nikolaos G. Fytas.

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Fytas, N., Theodorakis, P., Georgiou, I. et al. Critical aspects of the random-field Ising model. Eur. Phys. J. B 86, 268 (2013). https://doi.org/10.1140/epjb/e2013-40143-y

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