Spiral model, jamming percolation and glass-jamming transitions

TL;DR

The paper analyzes the Spiral Model, a kinetically constrained model exhibiting a unique glass-jamming transition characterized by a discontinuous percolation transition and diverging relaxation times, providing insights into glassy dynamics.

Contribution

It offers a detailed physical analysis of the Spiral Model and clarifies that its arguments remain valid despite recent critiques.

Findings

Discontinuous, compact percolation transition at the jamming point

Divergence of relaxation time faster than any power law

Validation of the model's analysis against recent criticisms

Abstract

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to an underlying jamming percolation transition which has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law, leading to a Vogel-Fulcher-like divergence of the relaxation time. Here we present a detailed physical analysis of SM, see [5] for rigorous proofs. We also show that our arguments for SM does not need any modification contrary to recent claims of Jeng and Schwarz [10].