Critical fan in the antiferromagnetic three-state Potts model

The three-state Potts model on a square lattice with general nearest-neighbor interaction and ferromagnetic second-neighbor interaction is studied. At zero temperature the model with antiferromagnetic nearest-neighbor interactions is mapped to the $F$ model. By comparing the excitations generated at nonzero temperature to those that lead to the eight-vertex model we obtain an explicit expression for the critical index describing such excitations and demonstrate the existence of a critical fan for ferromagnetic second-neighbor interactions. The model with purely nearest-neighbor interactions is critical only at zero temperature. Explicit expressions for the scaling indices of the color-color correlation function in the critical phase are also obtained. Phenomenological renormalization-group methods are applied to determine the general boundaries of the critical fan and to verify our expressions for critical indices. A physical system which might be expected to undergo a transition in the same universality class as that of the above model and to exhibit a critical phase is proposed: an equal mixture of krypton and xenon adsorbed on graphite.