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 \({\cal M} \times 2 {\cal N}\) square lattice with Brascamp-Kunz boundary conditions. We calculate ratios \(r_p(\rho)\) of \(p\)th coefficients of F for the infinitely long cylinder (\({\cal M} \to \infty\)) and the infinitely long Brascamp-Kunz strip (\({\cal N} \to \infty\)) at varying values of the aspect ratio \(\rho={(\cal M}+1) / 2{\cal N}\). Like previous studies have shown for the two-dimensional dimer model, the limiting values \(p \to \infty\) of \(r_p(\rho)\) exhibit abrupt anomalous behaviour 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.