  We investigate the phase diagram and critical behavior of a three-dimensional
lattice CP(N-1) model in the large-N limit. Numerical evidence of first-order
transitions is always observed for sufficiently large values of N, i.e. N>2 up
to N=100. The transition becomes stronger---both the latent heat and the
surface tension increase---as N increases. Moreover, on the high-temperature
side, gauge fields decorrelate on distances of the order of one lattice spacing
for all values of N considered. Our results are consistent with a simple
scenario, in which the transition is of first order for any N, including
N=\infty. We critically discuss the analytic large-N calculations that
predicted a large-N continuous transition, showing that one crucial assumption
made in these computations fails for the model we consider.
