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We study three-state Potts spins on a square lattice, in which all bonds areferromagnetic along one of the lattice directions, and antiferromagnetic alongthe other. Numerical transfer-matrix are used, on infinite strips of width $L$sites, $4 \leq L \leq 14$. Based on the analysis of the ratio of scaled massgaps (inverse correlation lengths) and scaled domain-wall free energies, weprovide strong evidence that a critical (Kosterlitz-Thouless) phase is present,whose upper limit is, in our best estimate, $T_c=0.29 \pm 0.01$. From analysisof the (extremely anisotropic) nature of excitations below $T_c$, we argue thatthe critical phase extends all the way down to T=0. While domain walls parallelto the ferromagnetic direction are soft for the whole extent of the criticalphase, those along the antiferromagnetic direction seem to undergo a softeningtransition at a finite temperature. Assuming a bulk correlation length varying,for $T>T_c$, as $\xi (T) =a_\xi \exp [ b_\xi (T-T_c)^{-\sigma}]$, $\sigma\simeq 1/2$, we attempt finite-size scaling plots of our finite-widthcorrelation lengths. Our best results are for $T_c=0.50 \pm 0.01$. We propose ascenario in which such inconsistency is attributed to the extreme narrowness ofthe critical region.Comment: 11 pages, 6 .eps figures, LaTeX with IoP macros, to be published in J  Phys

Kosterlitz Thouless transition in three-state mixed Potts ferro antiferromagnets