We investigate the critical behavior of three-dimensional ferromagnetic
CP(N-1) models, which are characterized by a global U(N) and a local U(1)
symmetry. We perform numerical simulations of a lattice model for N=2, 3, and
4. For N=2 we find a critical transition in the Heisenberg O(3) universality
class, while for N=3 and 4 the system undergoes a first-order transition. For
N=3 the transition is very weak and a clear signature of its discontinuous
nature is only observed for sizes L>50. We also determine the critical behavior
for a large class of lattice Hamiltonians in the large-N limit. The results
confirm the existence of a stable large-N CP(N-1) fixed point. However, this
evidence contradicts the standard picture obtained in the
Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter:
the presence of a cubic term in the effective LGW field theory for any N>2
would usually be taken as an indication that these models generically undergo
first-order transitions.Comment: 14 page
