In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration pc. This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles pr>pc. In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>pc and that near pc the shear modulus μ∼(p−pc)f, where the exponent f≈1.3 for two-dimensional lattices and f≈2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.
