The Legendre structure of the Parisi formula
classification
🧮 math.PR
math-phmath.MP
keywords
parisiformulainverselegendretemperatureallowsconcaveconjugate
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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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