The New Concept of Transitions by Breaking of Analyticity in a Crystallographic Model

  • Serge Aubry
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 8)


Phase transitions such as for example, incommensurate to commensurate modulated cristal [1] metal-insulator in Peierls quasi-one dimensional metals [2] , non registered to registered in adsorbed (or intersticial) atomic monolayers [3] exhibit new and unexpected features. Despite other problems like the zero-width central peak phenomena [4] , the Anderson-Mott metal-insulator transition [5] , the spin-glass transitions [6] look very different, we believe that the ideas that we develop in this paper, should be relevant to suggest a new approach to them. The main topic of this paper is the description of the phase transitions versus parameters of a very simple one-dimensional model for epitaxy at zero degree K. Most results are rigorous but their proofs which are too long, are omitted. We try to emphasize the role of two coupled concepts of defectibility and of frustration in the origin of this new kind of phase transitions.


Stationary Configuration Analytical Curf Phase Defect Erratic Trajectory Liouville Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Serge Aubry
    • 1
  1. 1.Laboratoire Léon Brillouin, Orme de MerisiersCEN-SACLAYGif-sur-YvetteFrance

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