Condensed Matter Physics, 2014, vol. 17, No. 4, 43003
Random-field Ising model: Insight from zero-temperature simulations
(Department of Chemical Engineering, Imperial College London, SW7 2AZ, London, United Kingdom)
(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.
random-field Ising model, finite-size scaling, graph theory
05.50.+q, 75.10.Hk, 64.60.Cn, 75.10.Nr