Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model
Mathematical Physics
2021-08-02 v1 math.MP
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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.
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Cite
@article{arxiv.2102.10178,
title = {Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model},
author = {Arka Adhikari and Christian Brennecke and Per von Soosten and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:2102.10178},
year = {2021}
}
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31 pages