Perturbative Interpretation of Adaptive Thouless-Anderson-Palmer Free Energy

TL;DR

This paper introduces a new derivation method for the adaptive TAP free energy that avoids difficult assumptions, using a high-temperature expansion of the Gibbs free energy, enhancing theoretical understanding.

Contribution

A novel derivation approach for adaptive TAP free energy that does not rely on restrictive assumptions, applicable beyond mean-field models.

Findings

Derivation of adaptive TAP free energy via high-temperature expansion.

Elimination of special assumptions in the derivation process.

Enhanced theoretical framework for adaptive TAP free energy.

Abstract

In conventional well-known derivation methods for the adaptive Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are difficult to mathematically justify except in some mean-field models, must be made. Here, we present a new adaptive TAP free energy derivation method. Using this derivation technique, without any special assumptions, the adaptive TAP free energy can be simply obtained as a high-temperature expansion of the Gibbs free energy.