Journal of Statistical Physics, Vol. 49, Nos. 1/2, 1987. p. 245-260.
We computed the specific heat of directed lattice animals using a Monte Carlo method for various animals sizes N, with N up to 100 on the square and N up to 125 on the simple cubic lattices. The specific heat as a function of the temperature for various animal sizes exhibits peaks which seem to approach a collapse transition temperature monotonically from below with increasing N. A least square fit together with finite-size scaling then gives both the transition temperature Tc and the specific heat exponent alpha for these two lattices. The
cyclomatic number distributions for the number of animals with fixed animal size N are also calculated and these seem to obey a scaling law for large N.