Large-N behavior of three-dimensional lattice CP N−1 models

We consider a three-dimensional lattice CPN−1 model, which corresponds to the lattice Abelian–Higgs model in the infinite gauge-coupling limit. We investigate its phase diagram and critical behavior in the large-N limit. We obtain numerical evidence that the model undergoes a first-order transition for suciently large values of N, i.e. for any 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 → ∞. 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.