Specific heat and collapse transition of branched polymers

We computed the specific heat of site lattice animals with nearest-neighbor attractive interaction for various animal sizes N, with N up to 80, on the simple-cubic lattice. For fixed N, the specific heat as a function of the temperature exhibits a peak at a temperature $T_m$(N) depending on N. As N increases, this peak gets higher and sharper and $T_m$(N) seems to approach a collapse transition temperature $T_c$ from below. A least-squares fit together with finite-size scaling then gives both the transition temperature $T_c$ and the specific-heat exponent α. The cycle-number distribution for the number of animals with fixed size N is also calculated. They seem to obey a scaling law for large N.