English

Short distance asymptotics for a generalized two-point scaling function in the two-dimensional Ising model

Mathematical Physics 2018-12-26 v2 Statistical Mechanics math.MP Exactly Solvable and Integrable Systems

Abstract

In the 1977 paper \cite{MTW} of B. McCoy, C. Tracy and T. Wu it was shown that the limiting two-point correlation function in the two-dimensional Ising model is related to a second order nonlinear Painlev\'e function. This result identified the scaling function as a tau-function and the corresponding connection problem was solved by C. Tracy in 1991 \cite{T}, see also the works by C. Tracy and H. Widom in 1998 \cite{TW}. Here we present the solution to a certain generalized version of the above connection problem which is obtained through a refinement of the techniques in \cite{B}.

Keywords

Cite

@article{arxiv.1808.02606,
  title  = {Short distance asymptotics for a generalized two-point scaling function in the two-dimensional Ising model},
  author = {Thomas Bothner and William Warner},
  journal= {arXiv preprint arXiv:1808.02606},
  year   = {2018}
}

Comments

9 pages, 2 figures

R2 v1 2026-06-23T03:27:28.299Z