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  • Open Access

q-Gaussian Crossover in Overlap Spectra toward 3D Edwards-Anderson Criticality

Yaprak Önder1,2, Abbas Ali Saberi3,1,*, and Roderich Moessner1

  • *Contact author: asaberi@constructor.university
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Phys. Rev. Lett. 136, 087103 – Published 26 February, 2026

DOI: https://doi.org/10.1103/sdbx-wx5t

Abstract

We introduce a spectral approach to characterizing the three-dimensional Edwards-Anderson spin glass. By analyzing the eigenvalue statistics of overlap matrices constructed from two-dimensional cross sections, we identify a crossover from the Wigner semicircle law at high temperatures toward a Gaussian distribution, which is consistently attained near the spin-glass critical point. Visible for different distributions of the random coupling, the Gaussian distribution can potentially serve as a robust spectral indicator of criticality. Remarkably, the spectral density is well described by Tsallis statistics, with the entropic index q evolving from q=−1 (semicircle, T=∞) to q=1 (Gaussian) at Tc, revealing a statistical structure inside the paramagnetic phase. We find q≤1 within numerical precision. While the local level statistics remain consistent with Gaussian orthogonal ensemble statistics, reflecting standard level repulsion, the temperature dependence appears mainly in the global spectral density. Our results present spectral statistics as a computationally efficient complement to multireplica correlator methods and provide a new perspective on cooperative and critical phenomena in disordered systems.

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Phys. Rev. Lett. 136, 087103– Published 26 February, 2026
  • Received 1 September 2025
  • Accepted 9 February 2026
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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 the Max Planck Society.

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