DYNAMIC MEAN-FIELD APPROXIMATION FOR THE RANDOM-BOND ISING-SPIN MODEL

A dynamic mean-field approximation, based on the standard updating scheme for the spin configurations in the Monte Carlo simulation, is developed to study a random-bond Ising spin model. The model studied is an Ising spin system on a two-dimensional square lattice with interactions between spins on nearest sites and a distribution of the bond interaction, P(J) = P(J)-delta(J - J0) + Q(J)-delta(J + J0), with P(J) + Q(J) = 1. The critical value of P(J) (P(J)c), above which a ferromagnetic order sets in, is found to be about 0.83, which is quite close to the result of the Monte Carlo simulation (0.85). Another critical value of P(J) (PBAR(J)c), below which an antiferromagnetic order sets in, is determined to be about 0.16.