Free energies of the spherical model of a spin glass

Abstract

Free energies g ( m, m s ) and f ( m, q ) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m , and SG order parameter m s and the Edwards-Anderson order parameter q . It is shown that g (0, m s ) and f (0, q ) below the transition temperature T g are constant in the ranges 0 ≦ m s ≦ m s 0 and 0 ≦ q ≦ q 0 respectively, where q 0 = (1 -− T T g ) = m 2 s 0 . The proper equilibrium values of m s ( = m s 0 ) and q ( d = q 0 ) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N -a ( a ≧ 0 ).