The two-dimensional q-state Potts model is subjected to a $Z_q$ symmetric disorder that allows for the existence of a Nishimori line. At $q=2,$ this model coincides with the $\pm J$ random-bond Ising model. For $q>\mathrm{}2,$ apart from the usual pure- and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality class is that of the ferromagnetic bond-disordered Potts model, and a strong disorder point which generalizes the usual Nishimori point. We numerically study the case $q=3,$ tracing out the phase diagram and precisely determining the critical exponents. The universality class of the Nishimori point is inconsistent with percolation on Potts clusters.

• Received 14 June 2001

DOI:https://doi.org/10.1103/PhysRevE.65.026113