Jamming as a topological satisfiability transition with contact number hyperuniformity and criticality

TL;DR

This paper models the jamming transition as a topological satisfiability problem, revealing that hyperuniformity and criticality arise from isostaticity and stability constraints, suggesting a new universality class for disordered systems.

Contribution

It introduces a minimal network model that explains jamming phenomena through topological and mechanical constraints, unifying hyperuniformity and criticality.

Findings

Hyperuniform contact distributions in the model match those of real jamming systems.

The model exhibits scale-free clusters and diverging length scales.

Results suggest a new universality class for jamming transitions.

Abstract

The jamming transition between flow and amorphous-solid states exhibits paradoxical properties characterized by hyperuniformity (suppressed spatial fluctuations) and criticality (hyperfluctuations), whose origin remains unclear. Here we model the jamming transition by a topological satisfiability transition in a minimum network model with simultaneously hyperuniform distributions of contacts, diverging length scales and scale-free clusters. We show that these phenomena stem from isostaticity and mechanical stability: the former imposes a global equality, and the latter local inequalities on arbitrary sub-systems. This dual constraint bounds contact number fluctuations from both above and below, limiting them to scale with the surface area. The hyperuniform and critical exponents of the network model align with those of frictionless jamming, suggesting a new universality class of non-equilibrium phase transitions. Our results provide a minimal, dynamics-independent framework for jamming criticality and hyperuniformity in disordered systems.