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APS » Journals » Rev. Mod. Phys. » Volume 58 » Issue 3
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Rev. Mod. Phys. 58, 765–788 (1986)

Ultrametricity for physicists

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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

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.

© 1986 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/RevModPhys.58.765
DOI:
10.1103/RevModPhys.58.765
PACS:
 
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