ENTROPIC ELASTICITY OF DILUTED CENTRAL FORCE NETWORKS

At zero temperature, the elastic constants of diluted central force ne tworks-are known to vanish at a concentration p(r) (of either sites or bonds) that is substantially higher than the corresponding geometric percolation concentration p(c). We study such diluted lattices at fini te temperatures and show that there is an entropic contribution to the moduli similar to that in cross-linked polymer networks. This entropi c elasticity vanishes at p(c) and increases linearly with T for p(c) < p < p(r). We also find that the shear modulus at fixed T vanishes as mu similar to (p - p(c))(f) with an exponent f that is, within numeric al uncertainty, the same as the exponent t that describes the conducti vity of randomly diluted resistor networks.