A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model

We use the Monte Carlo method to compute the number of trees with n edges in the Eden model on $d$-dimensional simple cubic lattices for $d=2,3,4,6,8,10$. We compare these numbers with the exact data derived by the enumeration method up to $n=12$ on the square lattice and up to $n=10$ on the cubic lattice. We find that for $d\geq3$, the computed values of the growth parameter for trees agree with the values that we derived earlier by the expansion in inverse powers of $2d-1$.