Classical ground states of symmetrical Heisenberg spin systems

Details Classical ground states of symmetrical Heisenberg spin systems Classical ground states of symmetrical Heisenberg spin systems

2002-09-06

arxiv.org/abs/cond-mat/0209157v2

Physics

Condensed Matter

35 pages, 8 figures Minor corrections of the first version, 1 additional reference

Scientific paper

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.

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