Properties of a generalized 3D O(2) model with suppression/enhancement of vortex strings

Using Monte Carlo and analytic methods, we map out the phase structure of a generalized 3D O(2) spin model with both ferromagnetic and antiferromagnetic couplings and both suppression and enhancement of vortex strings. The notion of sublattice vortex strings is introduced for the antiferromagnetic O(2) model, and the differences between their behavior and that of the uniform vortex strings are determined. The generalized model exhibits an interesting new type of critical behavior which reflects the presence of both continuous and discretely valued interactions, and the competition between them.