# Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet

## TL;DR

This paper develops a finite size scaling theory for first order phase transitions involving continuous symmetry breaking, validated by Monte Carlo simulations of the 3D XXZ Heisenberg antiferromagnet's spin-flop transition.

## Contribution

It introduces a Gaussian approximation with a degeneracy factor to predict universal finite size scaling behavior at first order transitions with symmetry breaking.

## Key findings

- Universal intersection points in moments and cumulants at the transition.
- Predicted degeneracy factor q=π matches numerical evidence.
- Finite size corrections scale as inverse volume.

## Abstract

Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite size behavior on a $L \times L \times L$ simple cubic lattice for the first order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension $L$ the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor $q$ that characterizes the relative degeneracy of the ordered phases. Our theory yields $q=\pi$, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first order phase transitions.