Solution of the generalised random energy model

Abstract

The generalised random energy model (GREM) is a spin-glass model which can be solved exactly. One can impose arbitrary pair correlations between the energies of configurations. For several examples (the Sherrington-Kirkpatrick model, the p spin-glass model, the Potts glass, spin-glass models on finite-dimensional lattices) the authors calculate the pair correlation between energies and solve the corresponding GREM. In all cases, the free energy of the GREM corresponding to a spin-glass model on a given lattice, has a simple expression in terms of the specific heat of the pure ferromagnetic model on the same lattice. Lastly they compare the correlations between three energy levels in the GREM and in spin-glass models.