A Morita Type Proof of the Replica-Symmetric Formula for SK

We give a proof of the replica symmetric formula for the free energy of the Sherrington-Kirkpatrick model in high temperature which is based on the TAP formula. This is achieved by showing that the conditional annealed free energy equals the quenched one, where the conditioning is given by an appropriate \(\sigma \)-field with respect to which the TAP solutions are measurable.