Natural Boundary for a Sum Involving Toeplitz Determinants
Mathematical Physics
2017-04-27 v1 Statistical Mechanics
Functional Analysis
math.MP
Abstract
In the theory of the two-dimensional Ising model, the diagonal susceptibility is equal to a sum involving Toeplitz determinants. In terms of a parameter k the diagonal susceptibility is analytic inside the unit circle, and the authors proved the conjecture that this function has the unit circle as a natural boundary. The symbol of the Toepltiz determinants was a k-deformation of one with a single singularity on the unit circle. Here we extend the result, first, to deformations of a larger class of symbols with a single singularity on the unit circle, and then to deformations of (almost) general Fisher-Hartwig symbols.
Cite
@article{arxiv.1502.04922,
title = {Natural Boundary for a Sum Involving Toeplitz Determinants},
author = {Craig A. Tracy and Harold Widom},
journal= {arXiv preprint arXiv:1502.04922},
year = {2017}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:1307.5913