Classification of integrable clusters of classical Heisenberg spins

Ameduri, Marco; Gerganov, Bogomil; Klemm, Richard A.

Classification of integrable clusters of classical Heisenberg spins

Authors

Ameduri, Marco

Gerganov, Bogomil

Klemm, Richard A.

Description

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.
6 pages, 2 figures