Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity

TL;DR

This paper investigates the dynamic critical behavior of nearly isostatic spring networks, revealing a length scale that influences their viscoelastic properties and response near the isostatic point.

Contribution

It introduces a dynamic critical length scale in nearly isostatic networks and relates it to viscoelastic response, supported by theoretical predictions and numerical verification.

Findings

Existence of a dynamic critical length scale near isostaticity

Proximity to isostaticity controls viscosity and shear modulus

Scaling relations connect the length scale to viscoelastic properties

Abstract

The isostatic state plays a central role in organizing the response of many amorphous materials. We demonstrate the existence of a dynamic critical length scale in nearly isostatic spring networks that is valid both above and below isostaticity and at finite frequencies, and use scaling arguments to relate the length scale to viscoelastic response. We predict theoretically and verify numerically how proximity to isostaticity controls the viscosity, shear modulus, and creep of random networks.