Novel non-ergodicity in the Potts spin glass

Ergodicity-breaking is stronger in a general p-state Potts than a conventional spin glass. Parisi and Sompolinsky treatments of such breaking are found to be non-equivalent for p>4, the former being inadequate. It is shown: (i) that Sompolinsky treatment in terms of two order functions q(x), Delta (x) yields a solution for all Potts dimensions: (ii) for p>4 the zero-field-cooled susceptibility acquires a discontinuity of order epsilon =p-4, whilst the field-cooled susceptibility is continuous as the transition and has the usual flat form beneath it.