Monte carlo study of the random-field Ising model

Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen [Phys. Rev. Lett. 61, 2635 (1988); 63, 1195 (1989)], we have studied the equilibrium properties of the thermal random-held Ising model on a cubic lattice in three dimensions. We have equilibrated systems of L x L x L spins, with values of L up to 32, and for these systems the cluster-dipping method appears to a large extent to overcome the slow equilibration seen in single-spin-flip methods. From the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite-size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06 +/- 0.07, gamma = 1.9 +/- 0.2, and <(gamma)over bar> = 2.9 +/- 0.2, where nu, beta, gamma, and <(gamma)over bar> govern the critical singularities in the correlation length, magnetization, and connected and disconnected susceptibilities, respectively.