Jamming as a random first-order percolation transition

TL;DR

This paper investigates the jamming transition as a mixed first-order percolation transition, analyzing its critical exponents across different dimensions through numerical simulations, and establishing key theoretical properties.

Contribution

It provides new numerical results for the exponents in four and five dimensions, and proposes that jamming is a mixed first-order percolation transition with specific critical exponents.

Findings

Jamming exhibits a mixed first-order percolation transition.

Critical exponents are determined for dimensions 2 to 5.

The upper critical dimension for jamming is proposed as 2.

Abstract

We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents $\beta =0$, $\gamma = 2$, $\alpha = 0$ and the finite size scaling exponent $\nu^* = 2/d$ for values of the spatial dimension $d \geq 2$. We argue that the upper critical dimension is $d_u=2$ and the connectedness length exponent is $\nu =1$.