  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.
