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The random Lorentz gas model exhibits paradoxical behavior in infinite dimensions. Finite-dimensional corrections reconcile percolation and glassiness, offering insights into complex system physics.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • The random Lorentz gas (RLG) is a fundamental model for studying percolation and glassiness.
  • A paradox arises in the infinite-dimensional limit (d → ∞), where RLG transitions are expected to be continuous (percolation) and discontinuous (glassiness).

Purpose of the Study:

  • To resolve the paradox in the infinite-dimensional limit of the RLG.
  • To investigate the role of finite-dimensional corrections in unifying percolation and glassy descriptions.
  • To analyze both static and dynamical solutions of the RLG in the d → ∞ limit.

Main Methods:

  • Analysis of static and dynamical solutions for the RLG in the d → ∞ limit.
  • Calculation of 1/d corrections to understand finite-dimensional effects.
  • Comparison of theoretical predictions with numerical results and mode-coupling theory (MCT).

Main Results:

  • Finite-dimensional perturbative and nonperturbative corrections are crucial for recovering percolation physics.
  • Theoretical descriptions struggle to encompass even perturbative corrections for the RLG.
  • Mode-coupling theory (MCT) captures the discontinuous nature of the d → ∞ RLG, despite quantitative discrepancies.

Conclusions:

  • The behavior of the RLG converges to the glassy description as dimensionality increases.
  • Finite-dimensional effects are essential for a complete understanding of RLG physics.
  • Insights gained pave the way for a comprehensive theory of finite-dimensional glasses.