Enumerations of lattice animals and trees

Abstract

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, $λ= 4.062570(8)$, for the growth constant of lattice animals, and, $λ_0 = 3.795254(8)$, for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, $ν= 0.64115(5)$, for the size exponent.