Diffusion on random clusters and the parasite problem

S. Wilke*, Y. Gefen, V. Ilkovic, A. Aharony, D. Stauffer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


In the parasite problem, a particle ('ant') diffuses randomly on a random percolation cluster in the limit of concentration to 0 ('lattice animal'). Monte Carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t(1/zA) with time t. The authors find zA approximately=3.4 on the simple cubic lattice and zA approximately=2.6 on the square lattice. This anomalous diffusion is in rough agreement with a generalisation of a suggestion by Alexander and Orbach (1982). Heuristic arguments in favour of this suggestion are given. Also, they look at corrections to scaling for concentrations equal to the percolation threshold.

Original languageEnglish
Pages (from-to)647-656
Number of pages10
JournalJournal of Physics A: Mathematical and General
Issue number3
StatePublished - 21 Feb 1984
Externally publishedYes


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