Statistics of lattice animals Original Research Article

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 re-sampling, 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 image. 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 image. 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.