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

Abstract

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-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.

arXiv comment11 pages, 1 figure

References in corpus (1)

• Discrete Painlevé equations for a class of \PVI $\tau$-functions given as U(N) averages

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