https://doi.org/10.1140/epjb/s10051-025-01030-0
Topical Review
Partition function for several Ising model interface structures
1
Department of Physics and Materials Science, University of Luxembourg, 30 Avenue des Hauts-Fourneaux, 4362, Esch-sur-Alzette, Luxembourg
2
Group for Computational Life Sciences, Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia
3
Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, OX1 3PU, Oxford, UK
4
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland
5
Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569, Stuttgart, Germany
Received:
30
June
2025
Accepted:
29
July
2025
Published online:
12
September
2025
We employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary conditions and allows for a physical interpretation in terms of coarse-grained quantities such as surface and point tensions. The resulting integrals contain all the information about finite-size effects; we extract them by careful asymptotic analysis using the steepest descent method. To this end, we exactly determine the steepest descent path and analyse its features. For the general class of integrals, which are usually found in the study of systems with inclined domain walls, knowledge of the steepest descent path is necessary to detect possible intersections with poles of the integrand in the complex plane.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-025-01030-0.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
