Entropic rigidity of randomly diluted two- and three-dimensional networks

In recent work, we presented evidence that site-diluted triangular central- force networks, at finite temperatures, have a nonzero shear modulus for al l concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energeti c) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangula r lattices, site-diluted square lattices, and site-diluted simple-cubic lat tices. We again find that these systems are rigid for all p >p(c) and that near p(c) the shear modulus mu similar to (p - p(c))(f), where the exponent f approximate to 1.3 for two-dimensional lattices and f approximate to 2 f or the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class a s the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion. [S1063-651X(99)07109-3].