This material has been published in "Condensed Matter Theories," vol. 19, E. Suraud, ed., Nova Science Publ., New York, 2004, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Nova Science Publ. This material may not be copied or reposted without explicit permission.

Karl E. Kürten and Christian Krattenthaler

Multistability and fractal properties of Hamiltonian lattice models

(10 pages)

Abstract. We investigate a particular N-particle system governed by a Hamiltonian. For this model, we enumerate all locally stable configurations, and as well all the possible displacements of the particles. This is achieved by Redfield-Pólya theory. In particular, we obtain that the number of locally stable configurations increases exponentially with N. The spectrum, which grows exponentially in a quasi self-similar manner is shown to be a fractal with fractal dimension d_f=1.55.

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