Dynamics of correlated forces in lattice model of granular solids near jamming

We investigate the dynamics of a simple lattice model of granular solids near jamming, using a Monte Carlo simulation that samples the ensemble of force networks consistent with a given average stress and distance from the isostatic point J. The Hamiltonian is simply the number of nearest-neighbor pairs that bear no force ("zero bonds"); as the simulation "temperature" decreases, the system is depleted of force-bearing contacts. We find that as point J approaches, various measures of the dynamics become extremely slow, with power-law divergences of characteristic times. We also observe dynamic heterogeneity, with a growing length scale defined by the spatial correlations of the persistence function for zero bonds. The model appears to approach point J at a finite temperature, at which various timescales diverge without an obvious corresponding divergence in the correlation length of some static order parameter, suggesting that this lattice model exhibits a hallmark of a dynamical glass transition.