Derivation of height field theory for the two-dimensional classical dimer model from a Grassmann-integral representation (opens in new tab)

The classical dimer model on bipartite lattices hosts a Coulomb phase, characterized by algebraic correlations and topological order. Its long-wavelength properties can be described by the fluctuations of a vector field with zero divergence, which, in two dimensions, is equivalent to a continuum height model. We show how this field theory can be derived constructively for both square and honeycomb lattices, starting from an exact representation ...