Random-field Ising model: Insight from zero-temperature simulations
Panagiotis E. Theodorakis, Nikolaos G. Fytas
We enlighten some critical aspects of the three-dimensional (d = 3) random-field Ising model from simulations performed at zero temperature.We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model.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 = L × L × L, where L denotes linear lattice size and L max = 156.Using as finite-size measures the sampleto-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 h c 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 random-field Ising model 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 energyand 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.
arXiv:1501.02338•Condensed Matter Physics•Dec 1, 2014•9 citations