Constructive Cavity Method

TL;DR

This paper demonstrates how the functional in the Parisi formula for the SK model's free energy can be derived from the Cavity Method under the assumption of a product state of independent Random Energy models.

Contribution

It provides a novel derivation of the Parisi functional using the Cavity Method with a specific independence assumption.

Findings

Derivation of the Parisi functional from the Cavity Method.

Connection between the Cavity Method and the Parisi formula.

Insight into the structure of the SK model's free energy.

Abstract

We show that the functional appearing in the celebrated Parisi formula for the free energy of the Sherrington-Kirkpatrick model can be found from the incremental free energy obtained by Cavity Method if one assumes that the state is a product of independent Random Energy models.