%0 Journal Article
%@ 1539-3755
%A Rios, Paolo
%A Caldarelli, Guido
%A Maritan, Amos
%A Seno, Flavio
%D 1996
%F eprints:1183
%I American Physical Society
%J Physical Review E
%K PACS: 05.40.+j, 02.50.-r  
%N 3
%P R2029-R2032
%T Optimal path and directed percolation
%U http://eprints.imtlucca.it/1183/
%V 53
%X An efficient transfer matrix technique is introduced to study directed optimal paths in two and three dimensions. The roughness exponent ζ is 0.6325±0.0007 for the two-dimensional case and ζ=0.555±0.008 for the three-dimensional one, in agreement with the recent conjecture ζ=ν⊥/ν∥, where ν⊥ and ν∥ are the correlation length exponents of directed percolation. Exactly solvable examples are also analyzed.