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Thouless–Anderson–Palmer Equations for the Ghatak–Sherrington Mean Field Spin Glass Model

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Abstract

We derive the Thouless–Anderson–Palmer (TAP) equations for the Ghatak and Sherrington model (J Phys C 10(16):3149–3156, 1977). Our derivation, based on the cavity method, holds at high temperature and at all values of the crystal field. It confirms the prediction of Yokota (J Phys Condens Matter 4(10):2615–2622, 1992).

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Acknowledgements

Both authors would like to thank Wei-Kuo Chen for several suggestions on a previous version of this work, including a simplification of the proof of Proposition 1. They thank two anonymous referees for many inputs that significantly improved the presentation of the paper. They also would like to thank Si Tang for early discussions and help with computer simulations. This research partially supported by NSF Grant CAREER DMS-1653552, Simons Foundation/SFARI (597491-RWC), and NSF Grant 1764421.

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  1. Department of Mathematics, Northwestern University, Evanston, USA

    Antonio Auffinger & Cathy Xi Chen

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  1. Antonio Auffinger
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  2. Cathy Xi Chen
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Correspondence to Antonio Auffinger.

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Communicated by Federico Ricci-Tersenghi.

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Auffinger, A., Chen, C.X. Thouless–Anderson–Palmer Equations for the Ghatak–Sherrington Mean Field Spin Glass Model. J Stat Phys 184, 22 (2021). https://doi.org/10.1007/s10955-021-02803-4

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