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

We use the Monte Carlo method to compute the number of trees with n edges i n 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 enumera tion method up to n = 12 on the square lattice and up to n = 10 on the cubi c lattice. We find that for d greater than or equal to 3, the computed valu es of the growth parameter for trees agree with the values that we derived earlier by the expansion in inverse powers of 2d - 1.