Renormalization-group study of the Hamiltonian version of the Potts model. III. Improved results for larger cells

The renormalization-group transformation, applied earlier to the Hamiltonian Potts model to study the crossover from second-order to first-order transition as the number of states $q$ increases, is extended by taking larger cells in the block transformation. The results improve systematically with increasing block size. The critical value of $q$ above which the transition is of first order, seems to converge to 5 instead of the exactly known value $q_c=4\mathrm{}$. The classical equivalents of the new couplings, which drive the system to the first-order transition, are discussed.