Natural Boundary for a Sum Involving Toeplitz Determinants

DOI10.1007/978-3-319-49182-0_29zbMATH Open1472.47023arXiv1502.04922OpenAlexW2098669383MaRDI QIDQ5269052

Publication date: 14 June 2017

Published in: Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1502.04922

zbMATH Keywords

Toeplitz determinants natural boundary \(k\)-deformation 2D Ising susceptibility

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Miscellaneous topics of analysis in the complex plane (30E99)

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