Scaling behaviour of lattice animals at the upper critical dimension
Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK
2 Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, 2 ave A. Chauvin, 95302 Cergy-Pontoise Cedex, France
3 Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany
Corresponding author: a r.Kenna@coventry.ac.uk
Published online: 15 September 2011
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011