THE SPHERICAL P-SPIN INTERACTION SPIN-GLASS MODEL - THE STATICS

The static properties of the spherical p-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step replica symmetry breaking. The transition from the replica symmetric solution to the replica replica symmetry broken one is either continuous or discontinuous in q1-q0 depending on the strength of the external magnetic field. The model can be solved explicitly for any p at any temperature and magnetic field. Below the transition we find an infinite number of metastable states.