## Abstract

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297–311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697–721, 1998) using Fredholm determinant representations of the correlation function and Wiener–Hopf approximation

results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058–1092, 1977).

results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058–1092, 1977).

Original language | English |
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Pages (from-to) | 672-683 |

Number of pages | 12 |

Journal | Journal of Statistical Physics |

Volume | 170 |

Issue number | 4 |

Early online date | 19 Dec 2017 |

DOIs | |

Publication status | Published - Feb 2018 |

## Keywords

- two-dimensional Ising model
- 2-Point function
- short distance expansion
- action integral