Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in a three-state Potts antiferromagnetic thin film

Abstract

Using Monte Carlo simulations and finite-size scaling, we study a three-state Potts antiferromagnet on a layered square lattice with two and four layers: ${L}_{z}=2$ and 4, respectively. As temperature decreases, the system develops quasi-long-range order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature ${T}_{c1}$. For ${L}_{z}=4$, as temperature is further lowered, a long-range order breaking the ${Z}_{6}$ symmetry develops at a second transition at ${T}_{c2}<{T}_{c1}$. The transition at ${T}_{c2}$ is also Berezinskii-Kosterlitz-Thouless-like, but has a magnetic critical exponent $\ensuremath{\eta}=1/9$ instead of the conventional value $\ensuremath{\eta}=1/4$. The emergent $U(1)$ symmetry is clearly demonstrated in the quasi-long-range ordered region ${T}_{c2}\ensuremath{\le}T\ensuremath{\le}{T}_{c1}$.