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

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Abstract

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, τ1 = 1.000 14(2), appears to exclude the conjecture τ1 = 1. The critical point and the exponents v and v have the same values as for the bulk problem.

Original languageEnglish
Pages (from-to)6055-6062
Number of pages8
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number33
DOIs
Publication statusPublished - 20 Aug 1999
Externally publishedYes

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