Critical aspects of the random-field Ising model

  • Nikolaos G. Fytas
  • Panagiotis E. Theodorakis
  • Ioannis Georgiou
  • Ioannis Lelidis
Regular Article

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 = L3, 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 hc, 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.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nikolaos G. Fytas
    • 1
    • 2
  • Panagiotis E. Theodorakis
    • 3
  • Ioannis Georgiou
    • 4
  • Ioannis Lelidis
    • 2
  1. 1.Applied Mathematics Research Centre, Coventry UniversityCoventryUK
  2. 2.Department of PhysicsUniversity of AthensAthensGreece
  3. 3.Department of Chemical EngineeringLondonUK
  4. 4.Institute for Theoretical Physics and Center for Computational Materials Science, Vienna University of TechnologyViennaAustria

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