Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

Area of Science:

• Statistical Mechanics
• Computational Physics
• Complex Systems

Background:

• Kinetically-constrained models (KCMs) like Kob-Andersen and Fredrickson-Andersen are crucial for understanding glassy dynamics.
• Determining the thermodynamic limit of critical jamming density has been computationally challenging.
• Distinguishing finite-size from finite-density corrections is essential for theoretical accuracy.

Purpose of the Study:

• To calculate corrections to the critical jamming density in KCMs.
• To differentiate between finite-density and finite-size effects.
• To introduce and validate a new, memory-efficient numerical algorithm for large-scale simulations.

Main Methods:

• Development of a novel numerical algorithm that generates only necessary data, minimizing computer memory usage.
• Simulation of systems significantly larger than previously achieved (exceeding 10^7 x 10^7 sites).
• Analysis of results to determine the nature of corrections to the thermodynamic limit.

Main Results:

• Corrections to the critical jamming density are identified as finite-density corrections, not finite-size corrections.
• The new algorithm demonstrates high efficiency and scalability for large system simulations.
• Results align with rigorous theoretical bounds on asymptotic corrections.
• The average number of sites initiating a critical droplet exceeds one.

Conclusions:

• Finite-density corrections are the primary factor influencing critical jamming density in the thermodynamic limit for KCMs.
• The novel algorithm offers a powerful tool for simulating extremely large systems in statistical mechanics.
• This work provides a clearer understanding of jamming phenomena in glassy systems.