Critical properties of a fractionally frustrated XY model on the square lattice

We study a fractionally frustrated XY model on the square lattice. This type of frustration is
induced by regularly placing a gauge $A_{ij}$ on each link of the lattice, with the requirement that the circulation $\sum_{ij \epsilon \square} A_{ij} = 2\pi f $ where $f$ is a fraction. The model is represented by the Hamiltonian
$$
H = - J \sum_{ij} \cos (\theta_i - \theta_j - A_{ij})
$$
where $\theta_i$ is the orientation of spin on $i$-th lattice site.
We study (via replica exchange Monte Carlo) how the Berezinskii-Kosterlitz-Thouless(BKT) phase of the conventional ($f=0$) XY model changes for general fractional $f$.


Ref:
T. Surungan, S. Masuda, Y. Komura and Y. Okabe, J. Phys. A: Math. Theor. 52 (2019) 275002.