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 $\tau$ which describes the behavior of the elastic stiffness near $p_c$ for $d=6\mathrm{}$ and obtain a lower bound on $\tau$ for $d<\mathrm{}6\mathrm{}$. $\tau$ is considerably higher than the conductivity exponent $t$, suggesting that the elastic problem belongs to a different universality class.

• Received 27 January 1984

DOI:https://doi.org/10.1103/PhysRevLett.52.1891