LOCAL DIRECTED PERCOLATION PROBABILITY IN 2 DIMENSIONS

Using the series expansion method and Monte Carlo simulation, we study the directed percolation probability on the square lattice V-n(0) = { (x; y) is an element of Z(2) : x + y even, 0 less than or equal to y l ess than or equal to n, -y less than or equal to x less than or equal to y). We calculate the local percolation probability P-n(l) defined a s the connection probability between the origin and a site (0, n). The critical behavior of P-infinity(l) is clearly different from the glob al percolation probability P-infinity(g) characterized by a critical e xponent Pg. An analysis based on the Pade approximants shows beta(l) = 2 beta(g) In addition, we find that the series expansion of P-2n(l) c an be expressed as a function of P-n(g).