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ORIGINAL RESEARCH article

Front. Phys.
Sec. Condensed Matter Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1473378
This article is part of the Research Topic Current Research On Spin Glasses View all 9 articles

Critical Droplets and Replica Symmetry Breaking

Provisionally accepted
Daniel L. Stein Daniel L. Stein *Charles M. Newman Charles M. Newman
  • New York University, New York City, United States

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

    We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states as predicted by replica symmetry breaking is equivalent to the presence of critical droplets whose boundaries comprise a positive fraction of edges in the infinite lattice.

    Keywords: spin glasses, ground states, Critical droplets, replica symmetry brealing, ground state interfaces

    Received: 30 Jul 2024; Accepted: 24 Oct 2024.

    Copyright: © 2024 Stein and Newman. 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: Daniel L. Stein, New York University, New York City, United States

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