Comment on “Spatial structure of states of self stress in jammed systems” by D. M. Sussman, C. P. Goodrich, and A. J. Liu, Soft Matter, 2016, 12, 3982
Sussman, Goodrich and Liu recently introduced a novel definition of states of self stress in packing-derived networks, and reported that the lengthscale that characterizes these states depends on the network connectivity z and spatial dimension đ as (z − 2đ)−0.8 in two dimensions, and as (z − 2đ)−0.6 in three dimensions. Here we derive an explicit expression for these particular states of self stress, and show that they are equivalent to the force response to a local dipolar force in random networks of relaxed Hookean springs, previously shown to be characterized by the lengthscale c ∼ (z − 2đ)−1/2. We conclude that the systems studied by Sussman et al. are insufficient in size to observe the correct scaling with connectivity of the characteristic lengthscale of states of self stress.