High Temperature Series Expansion of the d-Dimensional q-State Antiferromagnetic Potts Model

抄録

High temperature series expansions of the staggered susceptibility of the q-state antiferromagnetic Potts model (AFPM) on a d-dimensional hypercubic lattice are calculated. For arbitrary values of q and d, the transition temperatures and the critical exponents γ are determined by use of the ratio method and the Padé approximation. It is shown that the 3- and 4-state AFPM exhibit a second-order phase transition when d≥3, and the 5- and 6-state AFPM do when d≥4, etc. In the limit of infinite d, the transition temperature T_c is obtained rigorously as kT_c⁄J={log [2d⁄(2d−q)]}⁻¹ (k: the Boltzmann constant, J: the interaction parameter), and the ordered phase exists when d>q⁄2.