The square lattice Ising model on the rectangle II: finite-size scaling limit
Alfred Hucht
Abstract Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor . 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L × M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L , M → ∞ , T → T c , with fixed temperature scaling variable x ∝ ( T / T c − 1 ) M and fixed aspect ratio ρ ∝ L / M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T = T c we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys . B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen . 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.
arXiv:1701.08722•Journal of Physics A Mathematical and Theoretical•Apr 5, 2017•21 citations