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Phase transitions in a p-spin glass model: A numerical study

Prerak Gupta1,*, Auditya Sharma1,†, Bharadwaj Vedula1, J. Yeo2, and M. A. Moore3

  • *Contact author: prerak23@iiserb.ac.in
  • †Contact author: auditya@iiserb.ac.in
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Phys. Rev. E 114, 044116 – Published 8 October, 2026

DOI: https://doi.org/10.1103/clg9-2ln3

Abstract

We investigate the balanced M=4, p=4 spin-glass model for a one-dimensional long-range proxy for the finite-dimensional short-range p-spin glass model to examine the nature of the glass transition beyond mean-field theory. We perform large-scale Monte Carlo equilibrated simulations for both fully connected and power-law diluted versions of the model. The critical temperatures extracted from the finite-size scaling (FSS) analysis of spin-glass susceptibility are in good agreement with theoretical predictions for σ=0,0.25 and 0.55. For these values of the long-range exponent σ (which is the power of the decrease of the interactions between the spins with their separation), one might have expected that mean-field theory would provide a good description of the system. However, the spin-overlap distribution and the value of the λ-parameter do not provide numerical evidence for a one-step replica symmetry breaking (1RSB) phase transition. Instead, our results indicate a direct transition from the paramagnetic state to a full replica symmetry broken phase, with a renormalized value of λ≡ω2/ω1<1 suggesting a continuous FRSB transition, despite this ratio being equal to 2 at mean-field level. A value of λ>1 is required for the discontinuous 1RSB transition. We argue that strong finite-size effects and closely spaced transition temperatures remove the expected 1RSB transition for the system sizes which we can study. For values of the exponent σ=0.85 which roughly correspond to a three-dimensional system, we find that the renormalized value of λ is again less than 1, with no signs of either the 1RSB transition or the continuous FRSB transition, suggesting that the Kauzmann temperature TK in three dimensions might be zero, and the complete absence of phase transitions in structural glasses.

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Phys. Rev. E 114, 044116– Published 8 October, 2026
  • Received 1 May 2026
  • Accepted 26 August 2026
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