Stiffness jump in the generalized XY model on the square lattice

We study the thermal phase transitions in the generalized classical XY model on the two-dimensional square lattice using single-cluster Monte Carlo simulations. In particular, we examine the (spin-wave) stiffness (helicity modulus) jump at the transition between the low-temperature algebraic phases and the disordered high-temperature regime. Employing a finite-size scaling ansatz from conformal field theory to estimate the termination of the algebraic phases that does not require knowledge of the critical properties, we provide an unbiased estimate of the stiffness jump. Our results are in full accord with the Berzinskii-Kosterlitz-Thouless scenario, i.e., the jump in the helicity modulus does not depend explicitly on the strength of the nematic coupling, but relates directly to the vorticity of the vortex excitations that drive the phase transition. We comment on previous work on related models, where Berzinskii-Kosterlitz-Thouless transition temperatures were based on scaling assumptions contradicted by our findings.