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Series expansion of the directed percolation probability. (English) Zbl 0770.60091

Summary: 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 cluster size. An analysis based on Padé approximants gives estimates of the critical threshold and also of the critical exponent \(\beta\).

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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