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

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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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Acknowledgements

The work of P. S. is supported by the DFG grant SO 1724/1-1. Part of this work was written when A.A. was under the sponsorship of a Harvard University GSAS MGSTTRF. The research of H.-T. Y. is partially supported by NSF grant DMS-1855509 and a Simons Investigator award.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Arka Adhikari, Christian Brennecke, Per von Soosten & Horng-Tzer Yau

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  1. Arka Adhikari
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  2. Christian Brennecke
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  3. Per von Soosten
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  4. Horng-Tzer Yau
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Correspondence to Christian Brennecke.

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Communicated by Eric A. Carlen.

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Adhikari, A., Brennecke, C., von Soosten, P. et al. Dynamical Approach to the TAP Equations for the Sherrington–Kirkpatrick Model. J Stat Phys 183, 35 (2021). https://doi.org/10.1007/s10955-021-02773-7

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