Phase structure of interacting boson models in arbitrary dimension

We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f = n - 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f ≥ 2 even or odd), the models have both first- and second-order phase transitions only if f = 5, 9, 13, .... In the other f ≥ 2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials