Incommensurate vortices and phase transitions in two-dimensional XY models with interaction having auxiliary minima

We discuss if phase diagrams of the two-dimensional XY models in which the interaction of nearest planar spins is a nonmonotonic function of the angle u between them, V(u) = - Jcos(u) - Kcos(qu) can include a phase transition related to the dissociation of pairs of fractional vortices when q > 2.