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.
CITATION STYLE
Tracy, C. A., & Widom, H. (2017). Natural boundary for a sum involving toeplitz determinants. In Operator Theory: Advances and Applications (Vol. 259, pp. 703–718). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_29
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