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
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−.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013