Lattice animal enumeration as a test of detailed balance in the Clarke-Vvedensky model of epitaxial growth

Abstract

We simulated lattice animal configurations on the square lattice using the method of Clarke-Vvedensky in their epitaxial growth model. We keep a list of occupied sites according to their number of occupied nearest-neighbor sites. New animal configurations are generated by picking 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 particle at the picked site to a randomly chosen perimeter site of the cluster, without regard to the initial and final configurations of the cluster, except that it must remain connected, and continually updating the list. By comparing with exact enumeration results, we find that this method does not generate the correct animal configurations. We then show that the correct animal configurations can be generated by modifying the method to take into account the initial and final configurations of the clusters. Our results show that the Clarke-Vvedensky model of epitaxial growth does not satisfy detailed balance in the equilibrium limit.