title: Entropic rigidity of randomly diluted two- and three-dimensional networks.
abstract: 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>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 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.
authors.affiliation: Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.
authors.forename: M
authors.initials: M
authors.lastname: Plischke
authors.forename: D C
authors.initials: DC
authors.lastname: Vernon
authors.forename: B
authors.initials: B
authors.lastname: Joós
authors.forename: Z
authors.initials: Z
authors.lastname: Zhou