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Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature

It is proven that the ground state is unique in the Edwards-Anderson model for almost all continuous random exchange interactions, and any excited state with the overlap less than its maximal value has large energy in dimensions higher than two with probability one. Since the spin overlap is shown to be concentrated at its maximal value in the ground state, replica symmetry breaking does not occur in the Edwards-Anderson model near zero temperature.