Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model
| dc.creator | Witte, N. S. | |
| dc.date | 2007-05-04 | |
| dc.date.accessioned | 2026-07-07T10:35:46Z | |
| dc.date.available | 2026-07-07T10:35:46Z | |
| dc.description | 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. | |
| dc.description | 11 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0705.0557 | |
| dc.identifier | http://arxiv.org/abs/0705.0557 | |
| dc.identifier | J.Phys.A40:F491,2007 | |
| dc.identifier | doi:10.1088/1751-8113/40/24/F08 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/179835 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 82B20; 34M55; 33C45 | |
| dc.title | Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model | |
| dc.type | text |