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

Thomas Bothner; William  Warner

doi:10.1007/s11040-018-9296-y

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

School of Mathematics

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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 language	English
Article number	37 (2018)
Number of pages	14
Journal	Mathematical Physics, Analysis and Geometry
Volume	21
Early online date	12 Dec 2018
DOIs	https://doi.org/10.1007/s11040-018-9296-y
Publication status	Published - Dec 2018

Keywords

Ising model
generalized 2-point function
short distance expansion

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

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 Painlev{\'e} 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).",

keywords = "Ising model, generalized 2-point function, short distance expansion",

author = "Thomas Bothner and William Warner",

year = "2018",

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doi = "10.1007/s11040-018-9296-y",

language = "English",

volume = "21",

journal = "Mathematical Physics, Analysis and Geometry",

issn = "1572-9656",

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T1 - Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model

AU - Bothner, Thomas

AU - Warner, William

PY - 2018/12

Y1 - 2018/12

N2 - 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).

AB - 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).

KW - Ising model

KW - generalized 2-point function

KW - short distance expansion

U2 - 10.1007/s11040-018-9296-y

DO - 10.1007/s11040-018-9296-y

M3 - Article (Academic Journal)

SN - 1572-9656

VL - 21

JO - Mathematical Physics, Analysis and Geometry

JF - Mathematical Physics, Analysis and Geometry

M1 - 37 (2018)

ER -

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

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