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 thatmaps the ground-state of the systemto themaximum-flowoptimization 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 sizesV = L ×L ×L, 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 hc and the critical exponent v 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/v 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.
Bibliographical noteThis article is published in an open access journal and is available to download at: http://www.icmp.lviv.ua/journal/zbirnyk.80/43003/art43003.pdf
- Finite-size scaling
- Graph theory
- Random-field Ising model