# New Universality Class in three dimensions: the Antiferromagnetic $RP^2$ model

## TL;DR

This paper reports Monte Carlo simulations of the 3D $RP^2$ model with negative coupling, revealing a second order phase transition and identifying critical exponents, suggesting a new universality class.

## Contribution

The study introduces a new universality class in three dimensions through detailed simulation and critical exponent analysis of the $RP^2$ model with negative coupling.

## Key findings

- Second order phase transition observed
- Critical exponent $
u=0.784(8)$ measured
- Two magnetic-type relevant operators identified

## Abstract

We present the results of a Monte Carlo simulation of the $RP^2$ model in three dimensions with negative coupling. We observe a second order phase transition between the disordered phase and an antiferromagnetic, unfrustrated, ordered one. We measure, with a Finite Size Scaling analysis, the thermal exponent, obtaining $\nu=0.784(8)$. We have found two magnetic-type relevant operators whose related $\eta$ exponents are $0.038(2)$ and $1.338(8)$ respectively.