Elastic Properties of Random Percolating Systems

Abstract

We study the macroscopic elastic moduli of an elastic percolating network in the critical region. A microscopic elastic Hamiltonian is used, which contains a bending energy term. We find that the rigidity threshold of this system is identical to the percolation threshold ${p}_{c}$. By considering the elastic properties of elements of the infinite percolation cluster we calculate the critical exponent $\ensuremath{\tau}$ which describes the behavior of the elastic stiffness near ${p}_{c}$ for $d=6$ and obtain a lower bound on $\ensuremath{\tau}$ for $d<6$. $\ensuremath{\tau}$ is considerably higher than the conductivity exponent $t$, suggesting that the elastic problem belongs to a different universality class.