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Ultrametricity for physicists

R. Rammal, G. Toulouse, and M. A. Virasoro

R. Rammal

  • Centre de Recherches sur les Très Basses Températures, Centre National de la Recherche Scientifique, BP 166 X, 38042 Grenoble-Cédex, France

G. Toulouse

  • Ecole Supérieure de Physique et Chimie Industrielles, 10 rue Vauquelin, 75231 Paris, France

M. A. Virasoro

  • Dipartimento di Fisica, Universita di Roma I, I-00185 Roma, Italy

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Rev. Mod. Phys. 58, 765 – Published 1 July, 1986

DOI: https://doi.org/10.1103/RevModPhys.58.765

Abstract

Ultrametricity is a simple topological concept, but its appearance in the language of physicists is recent. This review provides all the elementary background (from mathematics, taxonomy, and statistical physics) and surveys the main fields of development (spin glasses, optimization theory). Static and dynamic aspects are covered. From present knowledge, one can already draw some tentative conclusions on the common causes for the occurrence of ultrametric structures in nature. Some perspectives on unresolved problems in physics and biology are also presented.

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Rev. Mod. Phys. 58, 765– Published 1 July, 1986

    © 1986 American Physical Society

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