Monte Carlo study of percolation on disordered triangular lattices

A simple model for amorphous solids, consisting of a mixed bond triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is studied here by using computational simulation. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of regular [attenuated] bonds ρ [1−ρ] (0≤ρ≤1) and (2) the factor r, which is defined as the ratio between the value of the conductivity associated to an attenuated bond and that corresponding to a regular bond (0≤r≤1). The results obtained show how the percolation properties of the disordered system are modified with respect to the standard random bond percolation problem (r=0).