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H 1 Geometric description of the spherical Spin-Glass Gibbs measures and temperature chaos

Auteurs : Ben Arous, Gérard (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Gibbs measure of many disordered systems at low temperature may exhibit a very strong dependance on even tiny variations of temperature, usually called “temperature chaos”. I will discuss this question for Spin Glasses. I will report on a recent work with Eliran Subag (Courant) and Ofer Zeitouni (Weizmann and Courant), where we give a detailed geometric description of the Gibbs measure at low temperature, which in particular implies temperature chaos for a general class of spherical Spin Glasses at low temperature. This question has a very long past in the physics literature, and an interesting recent history in mathematics. Indeed, in 2015, Eliran Subag has given a very sharp description of the Gibbs measure for pure p-spin spherical Spin Glasses at low temperature, building on results on the complexity of these spin glasses by Auffinger-Cerny and myself. This description (close to the so-called Thouless-Anderson-Palmer picture) excludes the existence of temperature chaos for the pure p-spin!! The recent work gives an extension of this very detailed geometric description of the Gibbs measure to the case of general mixed models, and shows that in fact the pure p-spin is very singular.

    Codes MSC :
    82B44 - Disordered systems (random Ising models, random Schrodinger operators, etc.)
    82D30 - Random media, disordered materials (including liquid crystals and spin glasses)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 11/09/2018
      Date de captation : 28/08/2018
      Collection : Research talks ; Probability and Statistics ; Mathematical Physics
      Format : MP4
      Durée : 00:52:15
      Domaine : Probability & Statistics ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-08-28_Arous.mp4

    Informations sur la rencontre

    Nom de la rencontre : Advances in Statistical Mechanics / Avancées en mécanique statistique
    Organisateurs de la rencontre : Arguin, Louis-Pierre ; Gayrard, Véronique ; Kistler, Nicola ; Kourkova, Irina
    Dates : 27/08/2018 - 31/08/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1855.html

    Citation Data

    DOI : 10.24350/CIRM.V.19441103
    Cite this video as: Ben Arous, Gérard (2018). Geometric description of the spherical Spin-Glass Gibbs measures and temperature chaos. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19441103
    URI : http://dx.doi.org/10.24350/CIRM.V.19441103


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