Replica optimization method for ground-state search of random spin systems

Abstract

A new method to find ground states is proposed for random spin systems. The efficiency of this method is confirmed numerically in the case of the two-dimensional Ising spin glass with the gaussian bond-distribution in a uniform field. Increase of computational time with respect to system size is moderate and well fitted by a power-law up to L = 32. Magnetizations are calculated for various magnetic fields using the new method. Size dependence of the susceptibility is found to be χ(L) ∝ L x with x = 0.476(5). This value of the exponent x is somewhat larger than the predicted value by the droplet argument.