Exploring Cluster Growth Using a Simple Domino Tiling

This paper and its deposited material explore clustering of 2 x 1 dimers (dominoes) subject to simple interactions and temperature. Much of the work in domino tilings has been statistical, combinatoric and thermodynamic in nature. Instead, here, the domino is used as a simple model of a non-spherical molecule to explore aggregation, rather as if the molecules were interacting in solution. As a result, the work does not look at how many ways there are to tile a plane, but at how the cluster evolves with different parameters in the potential that governs the clustering. These parameters include the rules used to select which of the many possible dominoes will be added to the cluster, and temperature. It is shown that qualitative changes in clustering behaviour occur with temperature, including affects on the shape of the cluster, vacancies and the domain structure.