# Antiferromagnetism in four dimensions: search for non-triviality

## TL;DR

This paper investigates how antiferromagnetic interactions influence phase transitions and critical behavior in four-dimensional statistical models, highlighting model-dependent effects on their continuum limits.

## Contribution

It explores the impact of antiferromagnetism on phase diagrams and critical phenomena in four-dimensional models, revealing different outcomes across Ising, O(4), and RP2 models.

## Key findings

- Antiferromagnetism significantly alters phase diagrams.
- Model-dependent differences in critical behavior.
- Implications for continuum limits in quantum field theories.

## Abstract

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between second order transition points and the continuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the O(4) Models with a second neighbour negative coupling, and the $\RP{2}$ Model. Different conclusions are obtained depending on the model.