LATTICE ANIMAL ENUMERATION AS A TEST OF DETAILED BALANCE IN THE CLARKE-VVEDENSKY MODEL OF EPITAXIAL-GROWTH

We simulated lattice animal con figurations on the square lattice usin g the method of Clarke-Vvedensky in their epitaxial growth model. We k eep a list of occupied sites according to their number of occupied nea rest-neighbor sites, New animal configurations are generated by pickin g sites from this list with probability proportional to exp(-B/k(B)T) where B is the number of occupied nearest-neighbors of that site, T is the temperature and k(B) is Boltzman's constant, and moving the parti cle at the picked site to a randomly chosen perimeter site of the clus ter, without regard to the initial and final configurations of the clu ster, except that it must remain connected, and continually updating t he list, By comparing with exact enumeration results, we find that thi s method does not generate the correct animal configurations. We then show that the correct animal configurations can be generated by modify ing the method to take into account the initial and final configuratio ns of the clusters. Our results show that the Clarke-Vvedensky model o f epitaxial growth does not satisfy detailed balance in the equilibriu m limit.