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We enlighten some critical aspects of the three-dimensional ($d=3$)random-field Ising model from simulations performed at zero temperature. Weconsider two different, in terms of the field distribution, versions of model,namely a Gaussian random-field Ising model and an equal-weight trimodalrandom-field Ising model. By implementing a computational approach that mapsthe ground-state of the system to the maximum-flow optimization problem of anetwork, we employ the most up-to-date version of the push-relabel algorithmand simulate large ensembles of disorder realizations of both models for abroad range of random-field values and systems sizes $\mathcal{V}=L\timesL\times L$, where $L$ denotes linear lattice size and $L_{\rm max}=156$. Usingas finite-size measures the sample-to-sample fluctuations of various quantitiesof physical and technical origin, and the primitive operations of thepush-relabel algorithm, we propose, for both types of distributions, estimatesof the critical field $h_{\rm c}$ and the critical exponent $\nu$ of thecorrelation length, the latter clearly suggesting that both models share thesame universality class. Additional simulations of the Gaussian random-fieldIsing model at the best-known value of the critical field provide the magneticexponent ratio $\beta/\nu$ with high accuracy and clear out the controversialissue of the critical exponent $\alpha$ of the specific heat. Finally, wediscuss the infinite-limit size extrapolation of energy- andorder-parameter-based noise to signal ratios related to the self-averagingproperties of the model, as well as the critical slowing down aspects of thealgorithm.

Random-field Ising model: Insight from zero-temperature simulations