Phase diagram of a square lattice model of XY spins with direction-dependent interactions

We study a generalization of the well-known classical two-dimensional square lattice compass model of XY spins (sometimes referred to as the 90∘ compass model), which interpolates between the XY model and the compass model. Our model possesses the combined C4 lattice and spin rotation symmetry of the compass model but is free of its fine-tuned subsystem symmetries. Using both field theoretic arguments and Monte Carlo simulations, we find that our model possesses a line of critical points with continuously varying exponents of the Ashkin-Teller type terminating at the four-state Potts point. Further, our Monte Carlo study uncovers that beyond the four-state Potts point, the line of phase transition is connected to the lattice-nematic Ising phase transition in the square lattice compass model through a region of first-order transitions.