Partition function for several Ising model interface structures

Alessio Squarcini (), Piotr Nowakowski (), Douglas B. Abraham and Anna Maciołek
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Alessio Squarcini: University of Luxembourg
Piotr Nowakowski: Division of Physical Chemistry, Ruđer Bošković Institute
Douglas B. Abraham: Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory
Anna Maciołek: Polish Academy of Sciences

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 9, 1-18

Abstract: Abstract 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. Graphical abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01030-0

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