Scaling behaviour of lattice animals at the upper critical dimension

C. Von Ferber*, D. Foster, H. P. Hsu, R. Kenna

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We perform numerical simulations of the lattice-animal problem at the upper critical dimension d = 8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.

Original languageEnglish
Pages (from-to)245-249
Number of pages5
JournalEuropean Physical Journal B
Issue number2
Publication statusPublished - 15 Sept 2011


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