SERIES EXPANSION OF THE DIRECTED PERCOLATION PROBABILITY

Using a transfer-matrix technique we obtain extended series expansion of the percolation probability for the directed site percolation problem on the square lattice. Our approach reveals a previously unsuspected connection between this problem and the enumeration of the number of ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean duster size. An analysis based on Pade approximants gives estimates of the critical threshold and also of the critical exponent beta.