A Morita type proof of the replica-symmetric formula for SK

TL;DR

This paper provides a new proof of the replica symmetric formula for the SK model's free energy at high temperature, utilizing the TAP formula and showing the equivalence of conditional annealed and quenched free energies.

Contribution

It introduces a Morita type proof connecting the TAP formula with the replica symmetric free energy calculation for the SK model.

Findings

Conditional annealed free energy equals quenched free energy

Proof based on TAP solutions and high-temperature regime

Establishes a new link between TAP and replica symmetry

Abstract

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.