Condensed Matter Physics, 2014, vol. 17, No. 4, 43003
DOI:10.5488/CMP.17.43003           arXiv:1501.02338

Title: Random-field Ising model: Insight from zero-temperature simulations
  P.E. Theodorakis (Department of Chemical Engineering, Imperial College London, SW7 2AZ, London, United Kingdom) ,
  N.G. Fytas (Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, United Kingdom)

We enlighten some critical aspects of the three-dimensional (d=3) random-field Ising model (RFIM) from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V=LxLxL, where L denotes linear lattice size and Lmax=156. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hmax and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian RFIM at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.

Key words: random-field Ising model, finite-size scaling, graph theory
PACS: 05.50.+q, 75.10.Hk, 64.60.Cn, 75.10.Nr

Full text [pdf] << List of papers