Classification of integrable clusters of classical Heisenberg spins

2005/02/14 by Marco Ameduri, Ameduri, Marco, Bogomil Gerganov +3
Chemistry · Physics and Astronomy · #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Other Condensed Matter (cond-mat.other) #cond-mat.other

paper · pdf · doi:10.48550/arxiv.cond-mat/0502323

6 pages, 2 figures

arxiv created 2005/02/14 · openalex publication_date 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this letter we present a general classification of integrable models of identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our constructive proof of integrability provides a solution scheme for the equations describing the time evolution of each spin. We show that for a broad class of Heisenberg couplings, it is possible to solve the equations of motion iteratively by building a hierarchy of spins, each of which precesses about the composite spin of the previous level. This leads to the identification of the frequencies of precession at each level.

Related

• The Physical Basis of Integrable Spin Models
• The classical spin triangle as an integrable system
• General method for finding ground state manifold of classical Heisenberg model
• Hamiltonian dynamics of classical spins
• Semiclassical mechanics of a nonintegrable spin cluster