Classification of integrable clusters of classical Heisenberg spins

Details Classification of integrable clusters of classical Heisenberg spins Classification of integrable clusters of classical Heisenberg spins

2005-02-14

arxiv.org/abs/cond-mat/0502323v1

Physics

Condensed Matter

Other Condensed Matter

6 pages, 2 figures

Scientific paper

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.

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