Dimers on the checkerboard: model, partition sum, and correlations

We present analytic results on a special dimer model on the {\em non-bipartite} checkerboard that does not allow for parallel dimers surrounding diagonal links. We report exact results on the enumeration of closed packed dimer coverings on finite checkerboard lattices under periodic boundary conditions. Further, we comment on the behavior of the dimer-dimer correlations and find that the correlations between any two dimers vanishes identically if the distance between them is larger than two unit cells.