Abstract
Using the series expansion method and Monte Carlo simulation, we study the directed percolation probability on the square lattice V n 0 ={ ( x , y ) ∈ Z 2 : x + y =even, 0 ≤ y ≤ n , - y ≤ x ≤ y }. We calculate the local percolation probability P n l defined as the connection probability between the origin and a site (0, n ). The critical behavior of P ∞ l is clearly different from the global percolation probability P ∞ g characterized by a critical exponent β g . An analysis based on the Pade approximants shows β l =2β g . In addition, we find that the series expansion of P 2 n l can be expressed as a function of P n g .
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