# Three-dimensional ferromagnetic CP(N-1) models

## TL;DR

This study explores the critical phenomena of three-dimensional ferromagnetic CP(N-1) models through numerical simulations, revealing different transition types depending on N and confirming a stable large-N fixed point.

## Contribution

It provides the first detailed numerical analysis of the phase transitions in 3D ferromagnetic CP(N-1) models for N=2, 3, and 4, and examines the large-N limit behavior.

## Key findings

- N=2 exhibits a second-order transition in the O(3) universality class.
- N=3 and 4 show first-order transitions, with N=3 being very weak.
- Large-N analysis confirms a stable CP(N-1) fixed point.

## Abstract

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.