Kosterlitz-Thouless transition in three-state mixed Potts ferro-antiferromagnets

We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix are used, on infinite strips of width L sites, 4 ≤ L ≤ 14. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz-Thouless) phase is present, whose upper limit is, in our best estimate, Tc = 0.29 ± 0.01. From analysis of the (extremely anisotropic) nature of excitations below Tc, we argue that the critical phase extends all the way down to T = 0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for T > Tc, as ξ(T ) = aξ exp [