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

TL;DR

This paper investigates the phase transition in a three-state mixed Potts model on a square lattice, providing evidence for a Kosterlitz-Thouless critical phase extending down to zero temperature, with implications for understanding anisotropic excitations.

Contribution

The study offers the first numerical evidence of a Kosterlitz-Thouless phase in a mixed Potts model and analyzes the anisotropic nature of excitations and phase boundaries.

Findings

Critical phase exists up to T_c ≈ 0.29

Critical phase likely extends down to T=0

Inconsistencies in T_c estimates due to narrow critical region

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, $4 \leq L \leq 14$. 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.