Classical ground states of symmetric Heisenberg spin systems

Autor(en): Schmidt, HJ
Luban, M
Stichwörter: MAGNETISM; Physics; Physics, Mathematical; Physics, Multidisciplinary
Erscheinungsdatum: 2003
Herausgeber: IOP PUBLISHING LTD
Journal: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volumen: 36
Ausgabe: 23
Startseite: 6351
Seitenende: 6378
Zusammenfassung: 
We investigate the ground states of classical Heisenberg spin systems which have point group symmetry. Examples are the regular polygons (spin rings) and the seven quasi-regular polyhedra including the five Platonic solids. For these examples, ground states with special properties, e.g. coplanarity or symmetry, can be completely enumerated using group-theoretical methods. For systems having coplanar (anti-) ground states with vanishing total spin we also calculate the smallest and largest energies of all states having a given total spin S. We find that these extremal energies depend quadratically on S and prove that, under certain assumptions, this happens only for systems with coplanar S = 0 ground states. For general systems the corresponding parabolas represent lower and upper bounds for the energy values. This provides strong support and clarifies the conditions for the so-called rotational band structure hypothesis which has been numerically established for many quantum spin systems.
ISSN: 03054470
DOI: 10.1088/0305-4470/36/23/306

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