# The square lattice Ising model on the rectangle II: Finite-size scaling limit

Author Hucht, Alfred 2017 See all Details

#### Abstract

Based on the results published recently [J. Phys. A: Math. Theor., 50(6):065201, 2017], the finite-size contributions to the free energy of the square lattice Ising model on the $L\times M$ rectangle with open boundary conditions in both directions are calculated exactly in the finite-size scaling limit $L,M\to\infty$, $T\to T_\mathrm{c}$, with fixed temperature scaling variable $x\propto(T/T_\mathrm{c}-1)M$ and fixed aspect ratio $\rho\propto L/M$. We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point $T=T_\mathrm{c}$ we confirm predictions from conformal field theory by Cardy & Peschel [Nucl. Phys. B, 300:377, 1988] and Kleban & Vassileva [J. Phys. A: Math. Gen., 24:3407, 1991]. 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.

### Details

Title The square lattice Ising model on the rectangle II: Finite-size scaling limit Hucht, Alfred 2017 Research Article eng 28 pages, 6 figures, second part of arXiv:1609.01963 2017-01-30 00:00:00 High Energy Physics · Lattice · Mathematical Physics · Statistical Mechanics · Condensed Matter
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