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July 2019 Thouless–Anderson–Palmer equations for generic $p$-spin glasses
Antonio Auffinger, Aukosh Jagannath
Ann. Probab. 47(4): 2230-2256 (July 2019). DOI: 10.1214/18-AOP1307

Abstract

We study the Thouless–Anderson–Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, $\langle \cdot \rangle_{N}$, into a mixture of conditional laws, $\langle \cdot \rangle_{\alpha,N}$. We show that the TAP equations hold for the spin at any site with respect to $\langle \cdot \rangle_{\alpha,N}$ simultaneously for all $\alpha $. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.

Citation

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Antonio Auffinger. Aukosh Jagannath. "Thouless–Anderson–Palmer equations for generic $p$-spin glasses." Ann. Probab. 47 (4) 2230 - 2256, July 2019. https://doi.org/10.1214/18-AOP1307

Information

Received: 1 May 2017; Revised: 1 August 2018; Published: July 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07114716
MathSciNet: MR3980920
Digital Object Identifier: 10.1214/18-AOP1307

Subjects:
Primary: 60G15, 82D30

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 4 • July 2019
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