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arXiv:1510.03414 [math.PR]AbstractReferencesReviewsResources

The Legendre structure of the Parisi formula

Antonio Auffinger, Wei-Kuo Chen

Published 2015-10-12Version 1

We show that the Parisi formula of the mixed $p$-spin model is a concave function of the squared inverse temperature. This allows us to derive a new expression for the Parisi formula that involves the inverse temperature and the functional order parameter as Legendre conjugate variables.

Comments: 20 pages
Categories: math.PR, math-ph, math.MP
Subjects: 60K35, 82B44
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