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Multiple levels of symmetry breaking
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  • Published: August 2000

Multiple levels of symmetry breaking

  • Michel Talagrand1 

Probability Theory and Related Fields volume 117, pages 449–466 (2000)Cite this article

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Abstract.

In the previous paper in this volume we have studied the p-spin interaction model just below the critical temperature, and we have rigorously proved several aspects of the physicists prediction that this model exhibits “one level of symmetry breaking”. In the present paper we show how to construct systems that exhibit an arbitrarily large, but finite number of “levels of symmetry-breaking”. As the temperature decreases, such systems exhibit many phase transitions, as the structure of the overlaps gains complexity. This phenomenon does not seem to have been described previously, even in the physics literature.

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Authors and Affiliations

  1. Equipe d'Analyse-Tour 46, ESA au CNRS no. 7064, Université de Paris VI, 4 place Jussieu, 75230 Paris Cedex 05, France (e-mail: mit.@ccr.jussieu.fr), , , , , , FR

    Michel Talagrand

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  1. Michel Talagrand
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Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000

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Talagrand, M. Multiple levels of symmetry breaking. Probab Theory Relat Fields 117, 449–466 (2000). https://doi.org/10.1007/s004400000070

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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/s004400000070

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  • Mathematics Subject Classification (1991): Primary 82A87; Secondary 60G15, 60E15
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