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arXiv · 0705.0557

Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

N. S. Witte
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Abstract

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $τ$-function of the sixth Painlevé system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-classical weights, for which the diagonal Ising correlations arise as the leading coefficient of the polynomials specialised appropriately. Here we demonstrate that the next-to-diagonal correlations of the anisotropic Ising model are evaluated as one of the elements of this isomonodromic system or essentially as the Cauchy-Hilbert transform of one of the bi-orthogonal polynomials.

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N. S. Witte. 2007-05-04. Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model. https://doi.org/10.1088/1751-8113/40/24/f08

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