# Universal behaviour of the glass and the jamming transitions in finite dimensions

## TL;DR

This paper presents a revised cell theory combining free volume and RFOT to analyze glass and jamming transitions in finite dimensions, revealing their coincidence and critical behavior with specific exponents.

## Contribution

It introduces a unified theoretical framework showing the coincidence of glass and jamming transitions in finite dimensions and characterizes their critical properties.

## Key findings

- Glass and jamming transitions coincide in finite dimensions.
- Jamming transition is described by RFOT with a diverging static length.
- Critical exponents are independent of dimension d.

## Abstract

We investigate the glass and the jamming transitions of hard spheres in finite dimensions $d$, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite $d$. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent $\nu=2/d$, which we verify through finite size scaling, and standard critical exponents $\alpha = 0$, $\beta = 0$ and $\gamma = 2$ independent on $d$.