Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.06722 |
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Sommario:
- In the present paper, we study the asymptotics of the Fredholm determinant $D(x,s)$ of the finite-temperature deformation of the sine kernel, which represents the probability that there is no particles on the interval $(-x/π,x/π)$ in the bulk scaling limit of the finite-temperature fermion system. The variable $s$ in $D(x,s)$ is related to the temperature. The determinant also corresponds to the finite-temperature correlation function of one dimensional Bose gas. We derive the asymptotics of $D(x,s)$ in several different regimes in the $(x,s)$-plane. A third-order phase transition is observed in the asymptotic expansions as both $x$ and $s$ tend to positive infinity at certain related speed. The phase transition is then shown to be described by an integral involving the Hastings-McLeod solution of the second Painlevé equation.