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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geprüft am 20.05.2024