Three-dimensional monopole-free CP(N-1) models: behavior in the presence of a quartic potential

We investigate the phase diagram and the nature of the phase transitions in a three-dimensional model characterized by a global SU(N) symmetry, a local U(1) symmetry, and the absence of monopoles. It represents a natural generalization of the gauge monopole-free (MF) CP N-1 model, in which the fixed-length constraint (London limit) is relaxed. We have performed Monte Carlo simulations for N = 2 and 25, observing a finite-temperature transition in both cases, related to the condensation of a local gauge-invariant order parameter. For N = 2 results for the MF model are consistent with a weak first-order transition. A continuous transition would be possible only if scaling corrections were anomalously large. For N = 25 the results in the general MF model are also consistent with a first-order transition, that becomes weaker as the size of the field-length fluctuations decreases.