Large-N behavior of three-dimensional lattice CPN−1 models. (13th March 2020) - Pelissetto, Andrea; Vicari, Ettore
Abstract: We consider a three-dimensional lattice CP N −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 sufficiently 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 . 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.