Renormalization-group study of the Ashkin-Teller-Potts model in two dimensions

The critical behavior of the $s$-state Ashkin-Teller-Potts model on a square lattice is studied for $s=3, 4, \mathrm{and} 5$, using a variational renormalization-group transformation of the type introduced by Kadanoff. For the $s=3\mathrm{}$ and $s=4\mathrm{}$ models, the transformation correctly predicts a continuous phase transition. The calculated values of the critical exponents and the transition temperature are consistent with the results obtained from other approaches. For $s=5\mathrm{}$, however, the transformation fails to detect the first-order transition that is known to occur.