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

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  • Åhag, P.
  • Czyż, R.
  • Lundow, P.H.

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.

Suggested Citation

  • Åhag, P. & Czyż, R. & Lundow, P.H., 2024. "On a generalised Lambert W branch transition function arising from p,q-binomial coefficients," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005167
    DOI: 10.1016/j.amc.2023.128347
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    References listed on IDEAS

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    1. Moussa Ahmia & Hacène Belbachir, 2018. "p, q-Analogue of a linear transformation preserving log-convexity," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(3), pages 549-557, September.
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