Competing nematic interactions in a generalized XY model in two and three dimensions

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of $2\pi/q$ between neighboring spins. We focus here on the $q=8$ case (while presenting new results for other values of $q$ as well) whose phase diagram is much richer than the well known $q=2$ case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in $q=2$, but also infinite order transitions involving intermediate, competition driven phases absent for $q=2$ and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a suficient condition for it to be of BKT type.