# Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields

## TL;DR

This paper calculates the two-loop free energy of three-dimensional antiferromagnets under combined external magnetic and staggered fields using effective field theory, providing a renormalized, model-independent result expressed in terms of measurable parameters.

## Contribution

It presents a two-loop order calculation of the free energy for antiferromagnets in external fields within a model-independent effective field theory framework.

## Key findings

- Analytic renormalization of free energy achieved.
- Explicit expression in terms of temperature and external fields.
- Results are renormalization group invariant.

## Abstract

Using a model-independent low-energy effective field theory, we calculate the free energy of three-dimensional antiferromagnets in a combination of mutually perpendicular external magnetic and staggered fields at the next-to-next-to-leading, two-loop order. Renormalization is carried out analytically, and the renormalization group invariance of the result is checked explicitly. The free energy is thus expressed solely in terms of temperature, the external fields, and a set of low-energy coupling constants, to be determined by experiment or by matching to the microscopic model of a given concrete material.