Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method, we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice. We determine critical lines belong to the three-dimensional XY universality class in variable ofθ (2θ) between the XY-ferromagnetic (nematic) and disordered states. Furthermore, the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class. The critical points are determined from the intersections of Binder ratios for various system sizes. With two sets of critical points obtained, we finally
construct the phase diagram on theΔ-J plane.