Local Directed Percolation Probability in Two Dimensions

抄録

Using the series expansion method and Monte Carlo simulation, we study the directed percolation probability on the square lattice V_n⁰= { (x, y) ∈ Z²:x+y=even, 0 ≤ y ≤ n, - y ≤ x ≤ y }.We calculate the local percolationprobability P_n^l defined as the connection probability between theorigin and a site (0, n). The critical behavior of P_∞^lis clearly different from the global percolation probability P_∞^g characterized by a critical exponent β^g.An analysis based on the Padé approximants shows β^l=2β^g.In addition, we find that the series expansion of P_2n^l can be expressed as a function of P_n^g.