Classical Mechanics of a Three Spin Cluster

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dc.creatorHoule, Paul A.
dc.creatorHenley, Christopher L.
dc.date2002-07-23
dc.date.accessioned2026-07-07T05:34:13Z
dc.date.available2026-07-07T05:34:13Z
dc.descriptionA cluster of three spins coupled by single-axis anisotropic exchange exhibits classical behaviors ranging from regular motion at low and high energies, to chaotic motion at intermediate energies. A change of variable, taking advantage of the conserved z-angular momentum, combined with a 3-d graphical presentation (described in the Appendix), produce Poincare sections that manifest all symmetries of the system and clearly illustrate the transition to chaos as energy is increased. The three-spin system has four families of periodic orbits. Linearization around stationary points predicts orbit periods in the low energy (antiferromagnetic) and high energy (ferromagnetic) limits and also determines the stability properties of certain orbits at a special intermediate energy. The energy surface undergoes interesting changes of topology as energy is varied. We describe the similiarities of our three spin system with the Anisotropic Kepler Problem and the Henon-Heiles Hamiltonian. An appendix discusses numerical integration techniques for spin systems.
dc.description18 pp, 14 figures
dc.identifierhttps://arxiv.org/abs/nlin/0207040
dc.identifierhttp://arxiv.org/abs/nlin/0207040
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80285
dc.subjectChaotic Dynamics
dc.subjectMesoscale and Nanoscale Physics
dc.titleClassical Mechanics of a Three Spin Cluster
dc.typetext

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