Force correlations near point J in a lattice model of jamming

We have constructed a lattice model of a jammed system in $d=2$ dimensions near the isostatic point (Point J). Adapting the Tighe model, we represent a jammed pack of particles as a regular hexagonal array, with repulsive forces between nearest neighbors. We generate near-isostatic jammed configurations by carrying out a Monte Carlo simulation with Tighe ``wheel moves'', which rearrange forces locally while preserving force balance on every particle. (Wheel moves correspond to a small dilation of a given particle.) The MC simulation is progressively biased towards the creation of ``missing contacts'', bonds which bear zero force. We reveal long-range correlations in the force network near Point J by determining for each particle the smallest ``collective move'' --- a set of wheel moves that taken together dilates the given particle, while preserving the existing missing contacts. The size of these collective moves diverges as Point J is approached.