Revision of upper estimate of percolation threshold on square lattice

Abstract

The more exact upper estimate of the percolation threshold for the {\it site problem} on the quadratic lattice ${\mathbb{Z}}^2$ have been found on the basis of the cluster decomposition. It is done by the number estimate of cycles on ${\mathbb{Z}}^2$ which maybe external boundaries of finite clusters

9 pages, 1 figure