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On a generalised Lambert W branch transition function arising from p,q-binomial coefficients
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, Poland.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-6291-5885
2024 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 462, article id 128347Article in journal (Refereed) Published
Abstract [en]

With only a complete solution in dimension one and partially solved in dimension two, the Lenz-Ising model of magnetism is one of the most studied models in theoretical physics. An approach to solving this model in the high-dimensional case (d>4) is by modelling the magnetisation distribution with p,q-binomial coefficients. The connection between the parameters p,q and the distribution peaks is obtained with a transition function ω which generalises the mapping of Lambert W function branches W0 and W−1 to each other. We give explicit formulas for the branches for special cases. Furthermore, we find derivatives, integrals, parametrizations, series expansions, and asymptotic behaviours.

Place, publisher, year, edition, pages
Elsevier, 2024. Vol. 462, article id 128347
Keywords [en]
Generalization of Lambert W function, Lenz-Ising model, Magnetization distribution, p, q-binomial coefficients, Special functions
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-214983DOI: 10.1016/j.amc.2023.128347Scopus ID: 2-s2.0-85172163818OAI: oai:DiVA.org:umu-214983DiVA, id: diva2:1804717
Available from: 2023-10-13 Created: 2023-10-13 Last updated: 2023-10-13Bibliographically approved

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Åhag, PerLundow, Per-Håkan

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