# Critical properties of the Antiferromagnetic \RP2$ model in three dimensions

## TL;DR

This paper investigates the critical behavior of the three-dimensional antiferromagnetic RP^2 model, analyzing symmetry breaking, critical exponents, and finite-size effects to understand its phase transition properties.

## Contribution

It provides a detailed analysis of the symmetry breaking pattern and offers a precise determination of critical exponents using correlation length measurements.

## Key findings

- Full breakdown of O(3) symmetry near criticality
- Accurate critical coupling and exponent estimates
- Comparison of methods for computing critical exponents

## Abstract

We study the behavior of the antiferromagnetic RP$^2$ model in $d=3$. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical point we observe a full breakdown of the O(3) symmetry of the action. Several methods for computing critical exponents are compared. We conclude that the most solid determination is obtained using a measure of the correlation length. Corrections-to-scaling are parameterized, yielding a very accurate determination of the critical coupling and a 5\% error measure of the related exponent. This is used to estimate the systematic errors due to finite-size effects.