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 language | English |
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Article number | 37 (2018) |
Number of pages | 14 |
Journal | Mathematical Physics, Analysis and Geometry |
Volume | 21 |
Early online date | 12 Dec 2018 |
DOIs | |
Publication status | Published - Dec 2018 |
Keywords
- Ising model
- generalized 2-point function
- short distance expansion