Collapse transition and cyclomatic number distribution of directed lattice animals

Abstract

We computed the specific heat of directed lattice animals using a Monte Carlo method for various animals sizesN, withN up to 100 on the square andN 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 increasingN. A least square fit together with finite-size scaling then gives both the transition temperature T_c and the specific heat exponent α for these two lattices. The cyclomatic number distributions for the number of animals with fixed animal sizeN are also calculated and these seem to obey a scaling law for largeN.