Natural Boundary for a Sum Involving Toeplitz Determinants

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.

17 pages. arXiv admin note: text overlap with arXiv:1307.5913

References in corpus (2)

• The diagonal Ising susceptibility
• On the diagonal susceptibility of the 2D Ising model

Cited by in corpus (4)

• On Functions of quasi Toeplitz matrices
• Cofactors and eigenvectors of banded Toeplitz matrices: Trench formulas via skew Schur polynomials
• Eigenvalues of the laplacian matrices of the cycles with one weighted edge
• Symmetric polynomials in the symplectic alphabet and their expression via Dickson--Zhukovsky variables