Equilibrium fluctuations in mean-field disordered models

Giampaolo Folena, Giulio Biroli, Patrick Charbonneau, Yi Hu, and Francesco Zamponi
Phys. Rev. E 106, 024605 – Published 5 August 2022

Abstract

Mean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the p-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.

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  • Received 15 February 2022
  • Accepted 24 June 2022

DOI:https://doi.org/10.1103/PhysRevE.106.024605

©2022 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Giampaolo Folena1,2, Giulio Biroli1, Patrick Charbonneau3,4, Yi Hu3, and Francesco Zamponi1

  • 1Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
  • 2James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
  • 3Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
  • 4Department of Physics, Duke University, Durham, North Carolina 27708, USA

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Issue

Vol. 106, Iss. 2 — August 2022

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