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
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
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