Ideal glass transition in a simple 2D lattice model

TL;DR

This paper introduces a simple 2D lattice model that exhibits glassy behavior, with a predicted and confirmed ideal glass transition characterized by diverging relaxation times and correlation lengths.

Contribution

The study provides a minimal lattice model demonstrating an ideal glass transition, supported by analytical predictions and numerical simulations confirming critical behavior.

Findings

Critical transition at density 0.1717 predicted by R matrix analysis.

Power-law divergence of relaxation time and susceptibility observed.

Finite-size scaling confirms divergence of correlation length.

Abstract

We present a simple lattice model showing a glassy behavior. $R$ matrix analysis predicts critical termination of the super-cooled fluid branch at density $\rho_g=0.1717$. This prediction is confirmed by dynamical numerical simulations, showing power-law divergences of relaxation time $\tau_{1/2}$, as well as the 4-susceptibility $\chi_4$ peak's location and height exactly at the predicted density. The power-law divergence of $\chi_4$ continues up to $\chi_4$ as high as $10^4$. Finite-size scaling study reveals divergence of correlation length accompanying the transition.