Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model

TL;DR

This paper introduces a dynamical proof of the TAP equations for the SK model at high temperature, linking the equations to the decay of correlation functions and extending to higher order correlations.

Contribution

It provides a novel dynamical derivation of the TAP equations and establishes decay bounds for higher order correlation functions in the SK model.

Findings

TAP equations follow from decay of two-point correlations

Decay bounds for three-point functions are established

Methodology applies to high-temperature regime of the SK model

Abstract

We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish the decay of higher order correlation functions. We illustrate this by proving a suitable decay bound on the three point functions from which we derive an analogue of the TAP equations for the two point functions.