Fluctuations and criticality in the random-field Ising model.

We investigate the critical properties of the d = 3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength h and system sizes V = L x L x L, with L ≤ 156. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength hc and the correlation length exponent v. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent a and the violation of the hyperscaling exponent π. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios β/v and γ/v, respectively. [ABSTRACT FROM AUTHOR]