# Phase transition induced for external field in tree-dimensional isotropic Heisenberg antiferromagnet

## TL;DR

This study employs mean-field and effective-field renormalization group methods to analyze phase transitions in a three-dimensional isotropic Heisenberg antiferromagnet under a magnetic field, revealing the effectiveness of larger clusters in these calculations.

## Contribution

It introduces a comparative analysis of MFRG and EFRG methods with different cluster sizes for the Heisenberg antiferromagnet under magnetic field, highlighting the advantages of EFRG.

## Key findings

- EFRG approach outperforms MFRG with larger clusters
- Critical frontier lines are obtained for simple cubic and BCC lattices
- Cluster size impacts the accuracy of phase boundary predictions

## Abstract

In this paper, we report mean-field and effective-field renormalization group calculations on the isotropic Heisenberg antiferromagnetic model under a longitudinal magnetic field. As is already known, these methods, denoted by MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic certain Bravais lattice. Our attention has been on the obtantion of the critical frontier in the plane of temperature versus magnetic field, for the simple cubic and the body-centered cubic lattices. We used clusters with $N=1,2,4$ spins so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. Consequently, the resulting frontier lines show that EFRG approach overcomes the MFRG problems when clusters of larger sizes are considered.