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ORIGINAL RESEARCH article

Front. Phys.
Sec. Condensed Matter Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1431810
This article is part of the Research Topic Current Research On Spin Glasses View all 6 articles

Tensor networks for p-spin models

Provisionally accepted
Benjamin Lanthier Benjamin Lanthier Jeremy Côté Jeremy Côté Stefanos Kourtis Stefanos Kourtis *
  • Université de Sherbrooke, Sherbrooke, Canada

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

    We introduce a tensor network algorithm for the solution of p-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the "easy" phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the p-spin model through lossless compression, all without explicit knowledge of the problem's structure.

    Keywords: Spin glass (theory), tensor network algorithms, Disordered magnetic systems, satisfiability (SAT), model counting

    Received: 13 May 2024; Accepted: 03 Oct 2024.

    Copyright: © 2024 Lanthier, Côté and Kourtis. 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: Stefanos Kourtis, Université de Sherbrooke, Sherbrooke, Canada

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