Universality class of central-force percolation

Abstract

We present a numerical study using a relaxation method of the elastic central-force percolation problem. Our data are consistent with this problem being in the same universality class as elastic bond-bending percolation. We find that the fractal dimension of the force-carying backbone is 1.64±0.03, which is indistinguishable from the value found in usual scalar percolation, or in elastic bond-bending percolation. The elastic moduli scale with an exponent f/ν=3.0±0.3, which is close to the corresponding exponent in the elastic bond-bending problem.