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

Abstract

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, $4\le L\le 14$. 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, $T_c=0.29\pm 0.01$. From analysis of the (extremely anisotropic) nature of excitations below $T_c$, 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 $T>T_c$, 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-width correlation lengths. Our best results are for $T_c=0.50\pm 0.01$. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.

11 pages, 6 .eps figures, LaTeX with IoP macros, to be published in J Phys A

References in corpus (1)

• A Measure of data-collapse for scaling

Cited by in corpus (3)

• Emergent O(n) Symmetry in a series of three-dimensional Potts Models
• Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
• Numerical study of the critical phases of the frustrated Z(5) model