  We investigate the phase diagram, and the nature of the phase transitions, of
three-dimensional monopole-free CP(N-1) models, characterized by a global U(N)
symmetry and a U(1) gauge symmetry, and the absence of monopoles. We present
numerical analyses based on Monte Carlo simulations for N=2,4,10,15, and 25. We
observe a finite-temperature transition in all cases, related to the
condensation of a local gauge-invariant order parameter. For N=2 we are unable
to draw any definite conclusion on the nature of the transition. The results
may be interpreted by either a very weak first-order transition or a continuous
transition with anomalously large scaling corrections. However, the results
allow us to exclude that the system develops the critical behavior of the O(3)
vector universality class, as it occurs in the standard three-dimensional CP(1)
model without monopole suppression. For N=4,10,15, the transition is of first
order, and significantly weaker than that observed in the presence of
monopoles. For N=25 the results are consistent with a conventional continuous
transition. We compare our results with the existing literature and with the
predictions of different field-theory approaches. Our results are consistent
with the scenario in which the model undergoes continuous transitions for large
values of N, in agreement with analytic large-N calculations.
