General method for finding ground state manifold of classical Heisenberg model

TL;DR

This paper introduces a comprehensive method for analyzing the ground state manifolds of classical Heisenberg models, including a proof of spiral states and a spectral classification approach, applicable to various interaction types.

Contribution

It provides a new analytical and algorithmic framework for determining ground states of classical Heisenberg models based on spectral properties and extends to anisotropic interactions.

Findings

Proved a spiral theorem for certain conditions.

Classified models using spectral properties related to ground states.

Developed analytical and algorithmic methods for different spectra.

Abstract

We investigate classical Heisenberg models with the translation symmetries of infinite crystals. We prove a spiral theorem, which states that under certain conditions there must exist spiral ground states, and propose a natural classification of all manageable models based on some "spectral properties," which are directly related to their ground state manifolds. We demonstrate how the ground state manifold can be calculated analytically for all spectra with finite number of minima and some with extensive minima, and algorithmically for the others. We also extend the method to particular anisotropic interactions.