Spanning a space in a quasi-one dimensional lattice vs a two-dimensional lattice with square banned sites

Abstract

Percolation thresholds in quasi-one and two dimensional systems were compared. In the former, one-way spanning is employed with a spanning cluster defined as an array that extends horizontally from one end of the lattice to the other. A four-corner checking procedure is introduced in this study to measure the percolation threshold in the corresponding twodimensional systems with square banned sites (2DSBS). The results indicate that the threshold values from the two methods converge suggesting that the quasi-1D system and the 2DSBS are equivalent topologically.