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ORIGINAL RESEARCH article

Front. Phys.
Sec. Condensed Matter Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1507250
This article is part of the Research Topic Current Research On Spin Glasses View all 11 articles

Damage spreading and coupling in spin glasses and hard spheres

Provisionally accepted
Koji Hukushima Koji Hukushima 1*Werner Krauth Werner Krauth 2
  • 1 The University of Tokyo, Komaba, Japan
  • 2 Laboratoire de Physique de l’Ecole normale supérieure, Faculté des Sciences et Ingénierie, Sorbonne Université, Paris, France

The final, formatted version of the article will be published soon.

    We study the connection between damage spreading, a phenomenon long discussed in the physics literature, and the coupling of Markov chains, a technique used to bound the mixing time.We discuss in parallel the Edwards-Anderson spin glass model and the hard-disk system, focusing on how coupling provides bounds on the extension of the paramagnetic and liquid phases. We also work out the connection between path coupling and damage spreading. Numerically, the scaling analysis of the mean coupling time determines a critical point between fast and slow couplings. The exact relationship between fast coupling and disordered phases has not been established rigorously, but we suggest that it will ultimately enhance our understanding of phase behavior in disordered systems.

    Keywords: spin glasses, Hard-sphere model, Markov Chains, Coupling times, Damage spreading, Thermodynamic phase transitions, Dynamic phase transitions

    Received: 07 Oct 2024; Accepted: 17 Dec 2024.

    Copyright: © 2024 Hukushima and Krauth. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Koji Hukushima, The University of Tokyo, Komaba, Japan

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