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Dynamical correlation functions in the Ising field theory
by István Csépányi, Márton Kormos
Submission summary
| Authors (as registered SciPost users): | István Csépányi |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2406.05100v2 (pdf) |
| Date submitted: | 2024-07-08 16:38 |
| Submitted by: | Csépányi, István |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report 1 by Dirk Schuricht on 2024-7-21 (Invited Report)
Report
The article studies the two-point correlation functions of the magnetisation in the Ising field theory at finite temperature. The authors perform a finite-temperature form factor expansion and provide a resummation of it in terms of Fredholm determinants, which can be viewed as a major achievement. This allows a detailed analysis, in particular a numerical evaluation. The obtained results are in perfect agreement with previous results in certain special and limiting cases. The manuscript very clearly presents the derivation and results. Thus I recommend publication in SciPost Physics.
I have two minor questions/remarks, that the authors should consider:
1. At short distances the results from the numerically evaluated Fredholm determinant are compared to conformal field theory predictions. I wonder whether it is possible to obtain the resulting scaling behaviour, like (4.1), analytically from the determinant.
2. The non-analyticity of the correlation length (5.14) shown in Fig. 5.8 originates from the switch of the leading exponential term in the expansion (5.11). Is it feasible to study the effect of the sub-leading term, ie, the crossing between the two leading exponentials in more detail?
Recommendation
Publish (meets expectations and criteria for this Journal)