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This study quantifies fluctuations in glass models with random first-order transitions. Analytical and numerical results show strong agreement, providing a framework for finite-size corrections in disordered systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • Mean-field models of glasses exhibiting random first-order transitions show complex fluctuations.
  • Previous work focused on critical scaling regimes, leaving other equilibrium conditions less explored.

Purpose of the Study:

  • To develop a fully quantitative framework for all equilibrium conditions in mean-field glass models.
  • To analyze Gaussian fluctuations of overlaps, distinguishing between thermal and heterogeneous contributions.

Main Methods:

  • Utilized the replica method to evaluate Gaussian fluctuations of overlaps.
  • Decomposed fluctuations into thermal (within-state) and heterogeneous (between-state) components.
  • Compared analytical findings with numerical simulations.

Main Results:

  • Achieved a robust quantitative framework applicable to all equilibrium conditions.
  • Demonstrated strong agreement between analytical predictions and numerical simulations for the p-spin spherical model, random orthogonal model, and random Lorentz gas.
  • Identified key finite-size corrections to mean-field treatments.

Conclusions:

  • The developed framework accurately captures fluctuations in paradigmatic glass models.
  • Provides a reliable method for understanding finite-size effects in disordered systems.
  • Validates the quantitative approach across different model systems.