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We derive exact finite-size corrections for the free energy $F$ of the Isingmodel on the ${\cal M} \times 2 {\cal N}$ square lattice with Brascamp-Kunzboundary conditions. We calculate ratios $r_p(\rho)$ of $p$th coefficients of Ffor the infinitely long cylinder (${\cal M} \to \infty$) and the infinitelylong Brascamp-Kunz strip (${\cal N} \to \infty$) at varying values of theaspect ratio $\rho={(\cal M}+1) / 2{\cal N}$. Like previous studies have shownfor 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 thefinite-size-expansion-coefficient ratios differ, however, between the twomodels.

journal of physics. a, mathematical and theoretical

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