  We give a complete rigorous proof of the full asymptotic expansion of the
partition function of the dimer model on a square lattice on a torus for
general weights $z_h, z_v$ of the dimer model and arbitrary dimensions of the
lattice $m, n$. We assume that $m$ is even and we show that the asymptotic
expansion depends on the parity of $n$. We review and extend the results of
Ivashkevich, Izmailian, and Hu [6] on the full asymptotic expansion of the
partition function of the dimer model, and we give a rigorous estimate of the
error term in the asymptotic expansion of the partition function.
