Finite-size scaling of free energy in the dimer model on a hexagonal domain

We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the box". The energy of configuration is given by the volume of the pile and the partition function is computed by the classical MacMahon formula or, more formally, by the determinant of Kasteleyn matrix. We use the expression for the partition function to derive the scaling behavior of free energy in the limit of lattice mesh tending to zero and temperature tending to infinity. We consider the cases of finite hexagonal domain, of infinite height box and coordinate-dependent Boltzmann weights. We obtain asymptotic expansion of free energy and discuss the universality and physical meaning of the expansion coefficients.