Directed lattice animals in 2 dimensions : numerical and exact results

We study several models of directed animals (branched polymers) on a square lattice. We present a transfer matrix method for calculating the properties of these directed animals when the lattice is a strip of finite width. Using the phenomenological renormalization, we obtain accurate predictions for the connective constants and for the exponents describing the length and the width of large animals (ν∥ = 9/11 and ν⊥ = 1/2). For a particular model of site animals, we present and prove some exact results that we discovered numerically concerning the connective constant and the eigenvector of the transfer matrix when the eigenvalue is one. We also propose a conjecture for the number of animals which generalizes the expression guessed by Dhar, Phani and Barma.