Large-N behavior of three-dimensional lattice CP(N-1) models

TL;DR

This study examines the phase transitions of three-dimensional lattice CP(N-1) models at large N, providing numerical evidence that transitions are first-order for all N, contrary to some analytic predictions of continuous transitions.

Contribution

The paper presents numerical evidence supporting first-order phase transitions in 3D lattice CP(N-1) models for all N, challenging previous large-N analytic predictions of continuous transitions.

Findings

Transitions are first-order for N>2 up to N=100.

Latent heat and surface tension increase with N.

Gauge fields decorrelate at short distances for all N.

Abstract

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.