# 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, 065201 (2017)], the universal 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 by 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 J. Phys. A: Math. Theor. 50, 265205 (2017) Research Article eng 31 pages, 6 figures, second part of arXiv:1609.01963, some text and references added, several small errors fixed, figure 5 changed, accepted 2017-01-30 00:00:00 · 2017-02-22 00:00:00 · 2017-04-27 00:00:00 High Energy Physics · Lattice · Mathematical Physics · Statistical Mechanics · Condensed Matter

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