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 Jᵢⱼ{≠}Jⱼᵢ. 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 {η}=[Jᵢⱼ{J}ⱼᵢ$]/[${J}ᵢⱼ²], we find a clear transition from ergodic dynamics at η{{{η}}}c=0.825 to a phase (η>{{{η}}}c$) where a finite fraction of the spins freezes. Only in the fully symmetric case {η}=1 is the entire system frozen.