The Legendre structure of the Parisi formula

Published 12 Oct 2015 in math.PR, math-ph, and math.MP | (1510.03414v2)

Abstract: 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 Parisi measure as Legendre conjugate variables.

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