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

Abstract

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