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  • Letter
  • Open Access

Interaction-correlated random matrices

Abbas Ali Saberi1,2,*, Sina Saber1, and Roderich Moessner2

  • *Contact author: ab.saberi@ut.ac.ir, saberi@pks.mpg.de
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Phys. Rev. B 110, L180102 – Published 22 November, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.L180102

Abstract

We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the finite-size statistics characterized by a heavy-tailed eigenvalue distribution whose extremes are governed by the Fréchet extreme value distribution for the case corresponding to a ferromagnetic Ising transition. The introduction of a finite density of nonlocal interactions restores standard random-matrix behavior. Suitably rescaled average extremes, playing a physical role as an order parameter, can thus discriminate aspects of the interaction structure; they also yield further nonuniversal information. In particular, the link between maximum eigenvalues and order parameters offers a potential route to resolving long-standing problems in statistical physics, such as deriving the exact magnetization scaling function in the two-dimensional Ising model at criticality.

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Outline

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Phys. Rev. B 110, L180102– Published 22 November, 2024
  • Received 21 July 2023
  • Revised 13 October 2024
  • Accepted 7 November 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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