Criticality of O(N) symmetric models in the presence of discrete gauge symmetries

TL;DR

This paper explores the critical behavior of 3D antiferromagnetic RP(N-1) models with O(N) symmetry and Z_2 gauge symmetry, revealing discrepancies between theoretical predictions and numerical results regarding the nature of phase transitions.

Contribution

It combines field-theoretical analysis and Monte Carlo simulations to challenge the assumption that gauge modes are irrelevant at criticality in models with discrete gauge symmetries.

Findings

No stable fixed point for N=4 in LGW analysis, suggesting first-order transition.

Numerical evidence indicates a continuous transition, contradicting theoretical predictions.

Gauge modes may influence critical dynamics more than previously assumed.

Abstract

We investigate the critical properties of the three-dimensional (3D) antiferromagnetic RP(N-1}) model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group (RG) flow of the most general Phi^4 theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_2 gauge symmetry.