2002/09/06 by Heinz-Juergen Schmidt, Marshall Luban, Schmidt, Heinz-Juergen +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Graph Theory Research #Condensed Matter (cond-mat) #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #cond-mat #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0209157
35 pages, 8 figures Minor corrections of the first version, 1 additional reference
openalex publication_date 2002/09/06 · arxiv created 2002/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.