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 |
|---|---|
| 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