Testing a model with an extended O(2) symmetry in two and three dimensions.

We investigate a model with an extended O(2) symmetry in two and three dimensions, using the combination of extensive Monte Carlo simulations and the finite-size scaling. On this basis, we establish rich phase diagrams, which are constituted by O(2) critical lines. From various prospectives, the ordered states on the phase diagrams can be classified into intraspecies and interspecies correlated phases, quasi-long-range and long-range ordered phases, or ferromagnetic and antiferromagnetic phases. We furthermore show that the dimensionality effect acts on not only the ordering property, but also the topological structure of the phase diagram.