Low-density series expansions for directed percolation II: The square lattice with a wall

Details Low-density series expansions for directed percolation II: The square lattice with a wall Low-density series expansions for directed percolation II: The square lattice with a wall

1999-06-03

arxiv.org/abs/cond-mat/9906037v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 1 figure

Scientific paper

10.1088/0305-4470/32/33/304

A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very accurate estimates for the critical point and exponents. In particular, the estimate for the exponent characterizing the average cluster length near the wall, $\tau_1=1.00014(2)$, appears to exclude the conjecture $\tau_1=1$. The critical point and the exponents $\nu_{\parallel}$ and $\nu_{\perp}$ have the same values as for the bulk problem.

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