Parisi-like order parameter in the spherical model of a spin glass

Abstract

An analysis of the grand canonical version of the spherical model for a spin glass (first studied by Kosterlitz, Thouless and Jones (1976)) shows that its spin glass phase can be characterized by an order parameter function. This is a consequence of the large spin length fluctuations permitted by the relaxation of the spherical constraint. Along with the distribution of order parameter values, the authors find a distribution function for the free energy whose variations are extensive, as well. Both distributions are reminiscent of those found in the Parisi solution and in the random energy model for the Ising spin glass. There are important differences from the solutions proposed for the Ising model. In particular, the set of overlaps does not possess an ultrametric solution.