# Bethe Ansatz for two-magnon scattering states in 2D and 3D Heisenberg-Ising ferromagnets

## TL;DR

This paper develops and applies generalized Bethe ansatz methods to analyze two-magnon scattering states in 2D and 3D Heisenberg-Ising ferromagnets, revealing that about half of the states fit the Bethe form and proposing modifications for the rest.

## Contribution

It introduces new Bethe ansatz approaches for higher-dimensional ferromagnets and addresses the treatment of non-Bethe states with a degenerative discrete-diffractive modification.

## Key findings

- Approximately 50% of states have a correct 2D Bethe form.
- About 75% of states in 3D have a generalized Bethe form.
- Remaining states are treated with a degenerative discrete-diffractive approach.

## Abstract

Various versions of the Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg-Ising ferromagnets. It is shown that for 2D square (3D qubic) finite-periodic or infinite lattices about a half (3/4) of states have a correctly 2D- (3D-) generalized Bethe form. The remaining scattering states are treated (on the infinite lattices only) within the degenerative discrete-diffractive modification of the Bethe ansatz previously suggested by the author.