Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model

Thomas Bothner*, William Warner

*Corresponding author for this work

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Abstract

n the 1977 paper of McCoy et al. (J. Math. Phys. 18, 1058–1092, 1977) it was shown that the limiting two-point correlation function in the two-dimensional Ising model is related to a second order nonlinear Painlevé function. This result identified the scaling function as a tau-function and the corresponding connection problem was solved by Tracy (Commun. Math. Phys. 142, 297–311, 1991), see also the works by Tracy and Widom (Commun. Math. Phys. 190, 697–721, 1998). Here we present the solution to a certain generalized version of the above connection problem which is obtained through a refinement of the techniques chosen in Bothner (J. Stat. Phys. 170, 672–683, 2018).
Original languageEnglish
Article number37 (2018)
Number of pages14
JournalMathematical Physics, Analysis and Geometry
Volume21
Early online date12 Dec 2018
DOIs
Publication statusPublished - Dec 2018

Keywords

  • Ising model
  • generalized 2-point function
  • short distance expansion

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