1999/06/03 by Iwan Jensen · 1 citation
Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Conjecture #Critical exponent #Directed percolation #Exponent #Geometry #Ising model #Lattice (music) #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Physics #Random Matrices and Applications #Scaling #Series (stratigraphy) #Series expansion #Social connectedness #Square (algebra) #Square lattice #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/32/33/304
8 pages, 1 figure
arxiv created 1999/06/03 · openalex publication_date 1999/08/11 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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, 1 = 1.00014(2), appears to exclude the conjecture 1 = 1. The critical point and the exponents || and have the same values as for the bulk problem.