On phase transition and vortex stability in the generalized XY models

We study a recent generalization proposed for the XY model in two and three dimensions. Using both, the continuum limit and discrete lattice, we obtained the vortex configuration and shown that out-of-plane vortex solutions are deeply jeopardized whenever the parameter of generalization, L, is increased. The critical temperature for such models is calculated using the self consistent harmonic approximation. In both, two- and three-dimensional cases, such a temperature decreases with raising L. Our results are also compared with other approximated methods available in the literature