Three-dimensional antiferromagnetic CP(N-1) models

TL;DR

This paper studies the critical behavior of three-dimensional antiferromagnetic CP(N-1) models, revealing a continuous transition for N=3 belonging to the O(8) universality class, supported by numerical and RG analyses.

Contribution

It establishes the universality class for the N=3 case and provides RG analysis showing no stable fixed points for N>3.

Findings

N=3 ACP(2) model exhibits a continuous transition in the O(8) universality class.

Numerical data confirms the O(8) universality class prediction.

RG analysis finds no stable fixed points for N>3.

Abstract

We investigate the critical behavior of three-dimensional antiferromagnetic CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude that the three-component ACP(2) model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP(2) and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N>3. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.