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...
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2024-12-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.17.6.162 |
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| author | István Csépányi, Márton Kormos |
| author_facet | István Csépányi, Márton Kormos |
| author_sort | István Csépányi, Márton Kormos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3bd1f627c3a74290afcfd0535f38cb43 |
| institution | OA Journals |
| issn | 2542-4653 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-3bd1f627c3a74290afcfd0535f38cb432025-08-20T01:54:50ZengSciPostSciPost Physics2542-46532024-12-0117616210.21468/SciPostPhys.17.6.162Dynamical correlation functions in the Ising field theoryIstván Csépányi, Márton KormosWe 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.https://scipost.org/SciPostPhys.17.6.162 |
| spellingShingle | István Csépányi, Márton Kormos Dynamical correlation functions in the Ising field theory SciPost Physics |
| title | Dynamical correlation functions in the Ising field theory |
| title_full | Dynamical correlation functions in the Ising field theory |
| title_fullStr | Dynamical correlation functions in the Ising field theory |
| title_full_unstemmed | Dynamical correlation functions in the Ising field theory |
| title_short | Dynamical correlation functions in the Ising field theory |
| title_sort | dynamical correlation functions in the ising field theory |
| url | https://scipost.org/SciPostPhys.17.6.162 |
| work_keys_str_mv | AT istvancsepanyimartonkormos dynamicalcorrelationfunctionsintheisingfieldtheory |