Glass-like Caging with Random Planes

TL;DR

This paper introduces a minimal, exactly solvable real-space model for glasses that reveals geometrical signatures of transitions and provides insights into activated processes and Gardner physics.

Contribution

It presents a new, analytically tractable model that captures key features of glass physics and transitions, bridging mean-field theory and finite-dimensional behavior.

Findings

Identifies geometrical signatures of dynamical and jamming transitions

Provides insight into the origin of activated processes in glasses

Links non-convexity to Gardner physics in standard glass formers

Abstract

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would therefore be beneficial. Here, we propose such a real-space model that is amenable to infinite-dimensional analysis and is exactly solvable at high and low densities in finite dimension. By joining analysis with numerical simulations, we uncover geometrical signatures of the dynamical and jamming transitions and provides insight into the origin of activated processes. Translating these findings to the context of standard glass formers further reveals the role played by non-convexity in the emergence of Gardner physics.