Percolation on Elastic Networks: New Exponent and Threshold

Bond percolation on elastic networks involving nearest-neighbor forces is studied by numerical simulations. With purely central forces, the bulk and shear moduli go to zero, with an exponent f, and at a threshold pcen, which are significantly higher than the exponent t and threshold pc of the corresponding purely isotropic force or the equivalent electrical conduction problem. An interesting crossover is observed when both central and isotropic forces are included.