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DY: Fachverband Dynamik und Statistische Physik

DY 33: Critical Phenomena and Phase Transitions

DY 33.9: Talk

Wednesday, March 18, 2015, 17:15–17:30, BH-N 334

Casimir force scaling functions in 2d Ising systems with open boundaries: The importance of corner contributions — •Fred Hucht and Felix M. Schmidt — Fakultät für Physik, Universität Duisburg-Essen, 47048 Duisburg

We consider the two-dimensional square lattice Ising model with free boundary conditions, aiming at universal critical Casimir force scaling functions. Surprisingly, no closed form solution exists for finite L_∥× L_⊥ lattices due to the lack of translational invariance in both directions. However, the exact partition function polynomial can be efficiently calculated from the determinant of a (4 L_∥L_⊥)-dimensional sparse matrix using arbitrary-precision integer arithmetics. For infinite systems, we derive exact expressions for the bulk, surface and corner free energies at arbitrary temperatures using q-products [1]. Combining these results, we derive universal finite-size-scaling functions of the Casimir force and the residual free energy for different values of the aspect ratio ρ = L_⊥/L_∥. We find a unusual logarithmic divergence of the residual free energy scaling function at x = t L_⊥→ 0, which is directly related to the logarithmic L-dependence of the free energy at criticality predicted by Cardy and Peschel [2].

[1] E. Vernier and J. L. Jacobsen, J. Phys. A: Math. Theor. 45, 045003 (2012).

[2] J. Cardy and I. Peschel, Nucl. Phys. B 300, 377 (1988).