On the equivalence of the Sompolinsky and Parisi solutions for the SK spin glass

Using simple properties of the Parisi overlap function P(q) the author demonstrates that the Parisi and Sompolinsky solutions are entirely equivalent both for Ising and isotropic spin glasses. Studying the notorious Potts model, he shows that existence of P(q) leads to important new criteria for the physical solutions of a replica approach, which supplement those based on the familiar stability analyses.