Effect of shape anisotropy on percolation of aligned and overlapping objects on lattices.

We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences regarding the percolation behavior of anisotropic shapes. We consider a prototypical anisotropic shape-rectangle-on a square lattice and show that, for rectangles of width unity (sticks), the percolation threshold is a monotonically decreasing function of the stick length, whereas, for rectangles of width greater than two, it is a monotonically increasing function.