The $q$-state Potts models in two dimensions are studied with the Monte Carlo renormalization-group method. The results are in agreement with known properties. Combining our data with the qualitative picture of Nienhuis, Berker, Riedel, and Schick, we obtain a consistent description of the behavior of these models, including nearly singular behavior for $q>\mathrm{}4\mathrm{}$ (as proposed by Kim and Joseph) and suggesting logarithmic corrections to scaling for $q=4\mathrm{}$.

• Received 29 November 1979

DOI:https://doi.org/10.1103/PhysRevB.21.4094