Directed lattices: site-to-bond conversion and its uses for the percolation and dilute polymer transitions

A method for conversion of directed site animals to their bond counterparts is used to significantly extend the number of such configurations in 2, 3, 4 dimensions, obtain their loop partition and study the singularity structure (for both dominant and subdominant singularities) of the corresponding dilute polymer transitions. A special property of bond directed configurations (equivalence lence of loop and bond perimeter partition) is exploited to obtain longer susceptibility series in 3 and 4 dimensions and the gap exponent estimate is refined into the intervals TANOPartly funded by SBF 341 (Aachen-Julich-Koln) and Reitoria Uni. Porto (Project 1-87)