A replica method for the deterministic spin model with long range interactions

We discuss the spin glass states of the deterministic spin model with long range anti-ferromagnetic interactions. To apply the replica method, the partial statistical summation with fixed overlap parameters is introduced. By this formulation, we find that the replica theory for this model reduces to that of the anti-Hebbian model in the long range limit, suggesting the existence of dynamical phase transition and glassy states. Results of simulated annealing are also presented to confirm these results. (author)