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

Abstract

Using Monte Carlo simulations and finite-size scaling, we study three-state Potts antiferromagnet on layered square lattice with two and four layers $L_z=2$ and $4$. 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 magnetic critical exponent $\hat{I}\cdot =1/9$ instead of the conventional value $\hat{I}\cdot =1/4$. The emergent $U(1)$ symmetry is clearly demonstrated in the quasi-long-range ordered region $T_{c2}\le T\le T_{c1}$.

6 pages, 10 figs, accepted by Phys. Rev. B