On the TAP equations via the cavity approach in the generic mixed $p$-spin models

Wei-Kuo Chen; Si Tang

doi:10.1007/s00220-024-04971-2

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arXiv · 2207.05203

On the TAP equations via the cavity approach in the generic mixed $p$-spin models

Wei-Kuo Chen·Si Tang

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Abstract

In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi's replica ansatz. In this work, we aim to investigate the validity of the TAP equations in the generic mixed $p$-spin model. By utilizing the ultrametricity of the overlaps, we show that the TAP equations are asymptotically satisfied by the conditional local magnetizations on the asymptotic pure states.

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BibTeX RIS

Wei-Kuo Chen, Si Tang. 2022-07-11. On the TAP equations via the cavity approach in the generic mixed $p$-spin models. https://doi.org/10.1007/s00220-024-04971-2

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