Finite-lattice Hamiltonian results for the phase structure of the Z (q) models and the q-state Potts models

We use our finite-lattice approach to study the phase transitions of the Hamiltonian formulation for the (1 + 1)-dimensional Z (q) models. We confirm the known result that these models possess two phases for q<q_c and three phases for q>=q_c. Our calculation, however, gives q_c=6, while the perturbative calculation predicts q_c=5. Similar calculations for the (1 + 1)-dimensional q-state Potts models for q=4, 5, and 8 failed to differentiate the second-order transition expected for q<=4 from the first-order transition expected for q>=5.