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Statics and Dynamics of Nonlinear Systems pp 126–143Cite as

The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil’s Staircase; Application to Metal-Insulator Transitions in Peierls Chains

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 47))

Abstract

We review results which have been obtained on the “transition by breaking of analyticity” in incommensurate structures, that is in other words the transition by the lattice locking of an incommensurate modulation. The critical physical quantities are described and their critical exponents which depends on the incommensurability ratio are given on an example. This transition is found in the Frenkel Kontorova model and its extension with many neighbour interactions and in a continuous two-wave model. It is also found in Peierls chains where it corresponds to the extinction of the Fröhlich conductivity. The locking of the incommensurate modulation implies that the devil’s staircase which describes the variation of the incommensurability ratio versus a parameter becomes complete.

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Authors and Affiliations

  1. C.E.N. Saclay, F-91191, Gif-Sur-Yvette Cédex, France

    S. Aubry

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  1. S. Aubry
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Editors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133, Milano, Italy

    Giorgio Benedek

  2. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-7000, Stuttgart, Fed. Rep. of Germany

    Heinz Bilz  & Roland Zeyher  & 

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© 1983 Springer-Verlag Berlin Heidelberg

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Aubry, S. (1983). The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil’s Staircase; Application to Metal-Insulator Transitions in Peierls Chains. In: Benedek, G., Bilz, H., Zeyher, R. (eds) Statics and Dynamics of Nonlinear Systems. Springer Series in Solid-State Sciences, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82135-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-82135-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82137-0

  • Online ISBN: 978-3-642-82135-6

  • eBook Packages: Springer Book Archive

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