Percolation in negative field and lattice animals

Yigal Meir*, Amnon Aharony, A. Brooks Harris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study in detail percolation in a negative ghos field, and show that the percolation model crosses over, in the presence of a negative field h, to the lattice-animal model, as predicted by the field theory. This was done by exact solutions in one dimension and on a Cayley tree, and series expansions in general dimension. We confirm the scaling picture near the percolation threshold, and study the extended scaling ansatz for all values of h in terms of the nonlinear scaling field gh. Estimates for gh are obtained as a function of h in all dimensions. We also show how information on percolation clusters in all concentrations up to the percolation threshold may be extracted by studying the critical behavior of the generalized susceptibilitiesk(p,h) near their critical point pc(h) as a function of h, and obtain data on the cluster distribution function and on the ratio of perimeter bonds to cluster bonds, for large clusters for all 0ppc. The crossover function is studied in one dimension, mean-field theory and the expansion.

Original languageEnglish
Pages (from-to)649-656
Number of pages8
JournalPhysical Review B-Condensed Matter
Issue number1
StatePublished - 1989


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