A generalisation of the honeycomb dimer model to higher dimensions

Linde, Moore, and Nordahl introduced a generalisation of the honeycomb dimer model to higher dimensions. The purpose this article is describe number structural properties generalised model. First, it shown that samples are in one-to-one correspondence with perfect matchings hypergraph. This leads Kasteleyn theory: partition function equals Cayley hyperdeterminant adjacency hypermatrix Second, we prove an identity which relates covariance matrix random height directly geometrical structure known planar case but new for It relies on more explicit formulation Sheffield's cluster swap made possible by Finally, use special give simplified proof strict convexity surface tension case.