A second moment method for high-temperature mean-field spin glasses

It is well known that in mean-field spin glasses, the annealed free energy typically does not agree with the quenched one, even at high temperature. We propose a suitable conditioning argument which leads to an evaluation of the quenched free energy by a conditional second moment method. The proper conditioning is on the solution of the TAP equations. Up to now, it has been worked out only for the SK-model, and it does not (yet) work in the full high-temperature regime. The method can probably be applied much wider.

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