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 for |k| < 1, 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.
Mathematics Subject Classification (2010). 47B35, 30E99, 82B20.
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Tracy, C.A., Widom, H. (2017). Natural Boundary for a Sum Involving Toeplitz Determinants. In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_29
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DOI: https://doi.org/10.1007/978-3-319-49182-0_29
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-49180-6
Online ISBN: 978-3-319-49182-0
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