Critical behaviour of anisotropic 'superelastic' central-force percolation

Abstract

The authors study central-force percolation on a triangular lattice where the bonds are springs that can freely rotate around the nodes. All bonds in one preferred direction are infinitely rigid. In the other two directions a proportion p of the springs chosen at random are infinitely rigid while the rest have a finite strength. For this specific problem, the threshold at which the network becomes infinitely rigid corresponds to the usual bond-percolation threshold of a square lattice and is therefore exactly equal to 0.5. They use a transfer-matrix algorithm to study the elastic modulus of strips of width ranging from 2 to 32 and length 10⁵. They obtain an estimate of the critical exponent relative to the scaling of the elastic moduli with the strip width 0.99+or-0.03, close to s/v for the corresponding isotropic electric problem.