Monte Carlo study of lattice animals inddimensions

A new Monte Carlo method, the incomplete-enumeration method, is used to calculate both the square radii of gyration 〈$R_N^2$〉 and the number of animals $a_N$ of size N up to N=30 in the case d=3 and N=20 in the cases d=4–7. We obtain about 2% accuracy for $a_N$ and 0.2% accuracy for 〈$R_N^2$〉 for the largest sizes N. For d=9 longer runs yield values of $a_N$ and 〈$R_N^2$〉 to better than 0.25% and 0.04% accuracy, respectively. Our data are consistent with upper critical dimension $d_c$=8 and with the Flory formula for all d<$d_c$.