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 $p_{\mathrm{cen}}$, which are significantly higher than the exponent $t$ and threshold $p_c$ 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.