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