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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

The lambda extensions of the Ising correlation functions C(M, N )

Résumé

We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions C(M, N) of the two-dimensional Ising model. In particular, using these one-parameter series to understand the deformation theory around selected values of λ, namely λ = cos(π m/n) with m and n integers, we show that these series yield perturbation coefficients, generalizing form factors, that are D-finite functions. As a by-product these exact results provide an infinite number of highly non-trivial identities on the complete elliptic integrals of the first and second kind. These results underline the fundamental role of Jacobi theta functions and Jacobi forms, the previous D-finite functions being (relatively simple) rational functions of Jacobi theta functions, when rewritten in terms of the nome of elliptic functions.
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Dates et versions

hal-03896285 , version 1 (13-12-2022)

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  • HAL Id : hal-03896285 , version 1

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S Boukraa, J.-M Maillard. The lambda extensions of the Ising correlation functions C(M, N ). 2022. ⟨hal-03896285⟩
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