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

arXiv comment31 pages

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Parisi formula for mixed $p$-spin models
• Some Properties of the Phase Diagram for Mixed $p$-Spin Glasses
• Thouless-Anderson-Palmer equations for the generic p-spin glass model
• On the stochastic calculus method for spins systems
• Un théorème limite pour les covariances des spins dans le modèle de Sherrington--Kirkpatrick avec champ externe

Cited by in corpus (3)

• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• The Two Point Function of the SK Model without External Field at High Temperature
• The Replica Symmetric Formula for the SK Model Revisited