Eur. Phys. J. B (2013) 86: 268 (2013)
https://doi.org/10.1140/epjb/e2013-40143-y

Regular Article

Critical aspects of the random-field Ising model

¹ Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK
² Department of Physics, University of Athens, Panepistimiopolis, 15784 Zografos, Athens, Greece
³ Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
⁴ Institute for Theoretical Physics and Center for Computational Materials Science, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

^a e-mail: nfytas@phys.uoa.gr

Received: 20 February 2013
Received in final form: 27 March 2013
Published online: 12 June 2013

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 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⁻.