Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model
| Autor: | Thomas Bothner, William Warner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics::Theory
generalized 2-point function FOS: Physical sciences Correlation function (astronomy) 01 natural sciences Primary 82B20 Secondary 70S05 34M55 0103 physical sciences Ising model Order (group theory) Point (geometry) 0101 mathematics Scaling Condensed Matter - Statistical Mechanics Mathematical Physics Mathematical physics Mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems Statistical Mechanics (cond-mat.stat-mech) 010102 general mathematics Mathematical Physics (math-ph) Function (mathematics) Connection (mathematics) Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems short distance expansion 010307 mathematical physics Geometry and Topology Exactly Solvable and Integrable Systems (nlin.SI) |
| Zdroj: | Bothner, T J & Warner, W 2018, ' Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model ', Mathematical Physics, Analysis and Geometry . https://doi.org/10.1007/s11040-018-9296-y Bothner, T & Warner, W 2018, ' Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model ', Mathematical Physics, Analysis and Geometry, vol. 21, 37 (2018) . https://doi.org/10.1007/s11040-018-9296-y |
| DOI: | 10.1007/s11040-018-9296-y |
| Popis: | 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}. Comment: 9 pages, 2 figures |
| Databáze: | OpenAIRE |
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