### Abstract

We revisit the question of the relation between entanglement, entropy, and area for harmonic lattice Hamiltonians which are the discrete version of real free scalar fields. For the cubic harmonic lattice Hamiltonian which yields the real Klein Gordon field in the continuum limit we establish a strict relationship between the surface area of a distinguished hypercube and the degree of entanglement between the hypercube and the rest of the lattice, without resorting to numerical means. We outline extensions of these results to longer ranged interactions, finite temperatures and for classical correlations in classical harmonic lattice systems.