Exact finite-size corrections in the dimer model on a cylinder

The exact finite-size corrections to the free energy F of the dimer model on lattice MxN with cylindrical boundary conditions have been derived for three cases where the lattice is completely covered by dimers: M=2M , N=2N ; M=2M-1 , N=2N ; and M=2M , N=2N-1 . For these types of cylinders, ratios rp(rho) of the pth coefficient of F have been calculated for the infinitely long cylinder ( M ->infinity ) and infinitely long strip ( N ->infinity ) at varying aspect ratios. As in previous studies of the dimer model on the rectangular lattice with free boundary conditions and for the Ising model with Brascamp-Kunz boundary conditions, the limiting values p -> infinity exhibit abrupt anomalous behaviour of ratios rp(rho) at certain values of rho. These critical values of rho and the limiting values of the finite-size expansion coefficient ratios vary between the different models.