Dynamic Critical Response in Damped Random Spring Networks

The isostatic state plays a central role in organizing the response of many amorphous materials. We construct a diverging length scale in nearly isostatic spring networks that is defined both above and below isostaticity and at finite frequencies and relate the length scale to viscoelastic response. Numerical measurements verify that proximity to isostaticity controls the viscosity, shear modulus, and creep of random networks.