MEAN-FIELD MONTE-CARLO APPROACH TO THE SHERRINGTON-KIRKPATRICK MODEL WITH ASYMMETRIC COUPLINGS

An alternative method is applied to the nonequilibrium zero temperature dynamics of a Sherrington-Kirkpatrick model with nonsymmetric random exchange couplings J(ij) not-equal J(ji). Based on exact stochastic single spin equations for the infinite system, this mean-field Monte Carlo approach avoids the strong finite size effects of the usual simulations for this problem. Varying the average symmetry eta = [J(ij)J(ji)]/[J(ij)2], we find a clear transition from ergodic dynamics at eta < eta(c) = 0.825 to a phase (eta > eta(c)) where a finite fraction of the spins freezes. Only in the fully symmetric case eta = 1 is the entire system frozen.