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

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Abstract
A new method to find ground states is proposed for random spin systems. It is applicable to systems with any boundary conditions, any bond distribution and any magnetic field. The efficiency of this method is confirmed numerically in the case of the two-dimensional Ising spin glass with Gaussian bond distribution in a uniform field. The introduction of more than two replicas improves the efficiency of the method considerably. It is also found that the renormalization process is effective. The increase in 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 field using the new method. The size dependence of the susceptibility is found to be chi (L) varies as Lx with x=0.476(5). This is somewhat larger than predictions using domain-wall renormalization group arguments.

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