Statistics of lattice animals

The scaling behavior of randomly branched polymers in a good solvent is studied in two to nine dimensions, modeled by lattice animals on simple hypercubic lattices. For the simulations, we use a biased sequential sampling algorithm with resampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. The partition sum (number of different animals) and gyration radii are estimated. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. (c) 2005 Elsevier B.V. All rights reserved.