Parisi function q(x) for spin glasses near Tc

Abstract

We compute the orderparameter function q(x) for the Sherrington-Kirkpatrick spin-glass to high accuracy near T=T c in zero external field. The free energy is calculated to order (T c −T) 7 . The overlap function dx/dq is parabolic near q=0. We show generally that q(x) involves only odd powers of x below its plateau. Hence the overlap distribution in strictly zero fields is symmetric with continuous derivatives at q=0 Calcul de la fonction parametre d'ordre q(x) pour un verre de spin de Sherrington-Kirkpatrick en champ nul pres de T c , l'energie libre etant developpee jusqu'a l'ordre (T c -T 7 ): la fonction de recouvrement dx/dq est parabolique au voisinage de q=0, et q(x) ne contient que des puissances impaires de x au-dessous de la region du plateau