A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

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Abstract

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297–311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697–721, 1998) using Fredholm determinant representations of the correlation function and Wiener–Hopf approximation
results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058–1092, 1977).
Original languageEnglish
Pages (from-to)672-683
Number of pages12
JournalJournal of Statistical Physics
Volume170
Issue number4
Early online date19 Dec 2017
DOIs
Publication statusPublished - Feb 2018

Keywords

  • two-dimensional Ising model
  • 2-Point function
  • short distance expansion
  • action integral

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