A Monte Carlo study of O(3) antiferromagnetic models in three dimensions

TL;DR

This study uses Monte Carlo simulations to analyze three different antiferromagnetic O(3) spin models in three dimensions, revealing that all observed phase transitions are of first order.

Contribution

It provides a comparative Monte Carlo analysis of three distinct antiferromagnetic O(3) models, identifying the nature of their phase transitions.

Findings

All phase transitions are of first order.

Different lattice structures and couplings were studied.

Vacua properties were discussed for each model.

Abstract

We study three antiferromagnetic formulations of the O(3) spin model in three dimensions by means of Monte Carlo simulations: 1. a two parameter $\sigma$ model with nearest and next to nearest neighbors couplings in a cubic lattice; 2. a face centered cubic lattice with nearest neighbors interaction; 3. a cubic lattice with a set of fully frustrating couplings. We discuss in all cases the vacua properties and analyze the phase transitions. Using Finite Size Scaling analysis we conclude that all phase transitions found are of first order.