Dynamical correlation functions in the Ising field theory
We study finite temperature dynamical correlation functions of the magnetization operator in the one-dimensional Ising quantum field theory. Our approach is based on a finite temperature form factor series and on a Fredholm determinant representation of the correlators. While for space-like separati...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2024-12-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.17.6.162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We study finite temperature dynamical correlation functions of the magnetization operator in the one-dimensional Ising quantum field theory. Our approach is based on a finite temperature form factor series and on a Fredholm determinant representation of the correlators. While for space-like separations the Fredholm determinant can be efficiently evaluated numerically, for the time-like region it has convergence issues inherited from the form factor series. We develop a method to compute the correlation functions at time-like separations based on the analytic continuation of the space-time coordinates to complex values. Using this numerical technique, we explore all space-time and temperature regimes in both the ordered and disordered phases including short, large, and near-light-cone separations at low and high temperatures. We confirm the existing analytic predictions for the asymptotic behavior of the correlations except in the case of space-like correlations in the paramagnetic phase. For this case we derive a new closed form expression for the correlation length that has some unusual properties: it is a non-analytic function of both the space-time direction and the temperature, and its temperature dependence is non-monotonic. |
|---|---|
| ISSN: | 2542-4653 |