Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries

We derive exact finite-size corrections for the free energy F of the Ising model on the M x 2N square lattice with Brascamp-Kunz boundary conditions. We calculate ratios r(p)(rho) of pth coefficients of F for the infinitely long cylinder (M -> infinity) and the infinitely long Brascamp-Kunz strip (N -> infinity) at varying values of the aspect ratio rho = (M+ 1)/2N. Like previous studies have shown for the two-dimensional dimer model, the limiting values p -> infinity of r(p)(rho) exhibit abrupt anomalous behavior at certain values of rho. These critical values of rho and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models.