Effective-medium theory of percolation on central-force elastic networks

Abstract

We show that effective-medium theory gives an excellent description of regular lattices when nearest-neighbor central-force springs are present with probability p. Effective-medium theory shows that all the elastic constants go to zero at $p_{\mathrm{cen}={\mathrm{dp}}_c}$ where d is the dimension and $p_c$ is the effective-medium estimate of the ordinary percolation threshold.