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 $p_c.$ This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles $p_r>p_c.$ 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 $p>\mathrm{}{p}_c$ and that near $p_c$ the shear modulus $\mu \sim (p-p_c{)}^f,$ where the exponent $f\approx 1.3$ for two-dimensional lattices and $f\approx 2$ 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.

• Received 4 March 1999

DOI:https://doi.org/10.1103/PhysRevE.60.3129