Exact solution of Potts random energy models with weak connectivity and of the many-states Potts spin glass

The author generalises Derrida's random energy model to the Potts spin glass with p-spin interactions in the limit of large p. He solves the model exactly for the cases of strong and weak connectivity. In the latter case he shows how to solve the model using replicas and obtains a solution for the value of the set of order parameters Q r1. . .rs alpha 1. . . alpha s . He then derives the large-q limit of the ordinary q-state Potts spin glass on a lattice with finite connectivity.