On a generalised Lambert W branch transition function arising from p,q-binomial coefficients

P. Åhag, R. Czyż and P.H. Lundow

Applied Mathematics and Computation, 2024, vol. 462, issue C

Abstract: 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.

Keywords: Generalization of Lambert W function; Lenz-Ising model; Magnetization distribution; p,q-binomial coefficients; Special functions (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005167

DOI: 10.1016/j.amc.2023.128347

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