Renormalization-group study of the Hamiltonian version of the Potts model

The phase transition of the classical two-dimensional Potts model, in particular the order of the transition as the number of components $q$ increases, is studied by constructing renormalization-group transformations on the equivalent one-dimensional quantum problem. It is shown that the block transformation with two sites per cell indicates the existence of a critical $q_c$ separating the small-$q$ and large-$q$ regions with different critical behaviors. The physically accessible fixed point for $q>\mathrm{}{q}_c$ is a discontinuity fixed point where the specific-heat exponent $\alpha =1\mathrm{}$, and therefore the transition is of first order.