The anisotropic Ising correlations as elliptic integrals: duality and differential equations

We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers–Wannier duality to anisotropic correlation functions, and the linear differential equations for thes...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-10, Vol.49 (43), p.434004
Main Authors: McCoy, B M, Maillard, J-M
Format: Article
Language:English
Subjects:
Physics
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Summary:We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers–Wannier duality to anisotropic correlation functions, and the linear differential equations for these anisotropic correlations. More precisely, we show that the anisotropic correlation functions are homogeneous polynomials of the complete elliptic integrals of the first, second and third kind. We give the exact dual transformation matching the correlation functions and the dual correlation functions. We show that the linear differential operators annihilating the general two-point correlation functions are factorized in a very simple way, in operators of decreasing orders.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/43/434004