Journal
ANNALS OF PROBABILITY
Volume 47, Issue 4, Pages 2230-2256Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-AOP1307
Keywords
Spin glasses; TAP; random measures; ultrametricity; cluster decomposition
Categories
Funding
- NSF [DMS-1597864, OISE-1604232]
- NSF CAREER [DMS-1653552]
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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, <.>(N), into a mixture of conditional laws, <.>(alpha,N). We show that the TAP equations hold for the spin at any site with respect to <.>(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.
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