Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 49: Statistical Physics: General

DY 49.10: Vortrag

Freitag, 9. September 2022, 12:00–12:15, H20

The square-lattice Ising model on the rectangle — •Fred Hucht — Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg

For the square-lattice Ising model, the universal critical Casimir potential and force scaling functions can be calculated exactly for many geometries and boundary conditions. We present a recent exact solution of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions [1], in terms of the determinant of a M/2 × M/2 Hankel matrix H. The M−1 independent matrix elements of H are Fourier coefficients of a certain symbol function, which is given by the ratio of two characteristic polynomials. These polynomials are associated to the different directions of the system, encode the respective boundary conditions, and are directly related through the symmetry of the considered Ising model under exchange of the two directions. This representation is a major simplification of earlier results [2,3].

[1] A. Hucht, J. Phys. A: Math. Theor. 54, 375201 (2021). arXiv:2103.10776.

[2] A. Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017). arXiv:1609.01963, erratum [4].

[3] A. Hucht, J. Phys. A: Math. Theor. 50, 265205, (2017). arXiv:1701.08722.

[4] A. Hucht, J. Phys. A: Math. Theor. 51, 319601 (2018).