Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917714280316928 |
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| author | Seong, Kihoon |
| author_facet | Seong, Kihoon |
| contents | We study singular Gibbs measures for the three-dimensional Schrödinger-wave system, also known as the Yukawa system. Our primary result is the phase transition between weak and strong coupling cases, a phenomenon absent in one- and two-dimensional cases. Therefore, the three-dimensional model turns out to be critical, exhibiting the phase transition. In the weak coupling case, the Gibbs measure can be normalized as a probability measure and is shown to be singular with respect to the Gaussian free field. Conversely, in the strong coupling case, the Gibbs measure cannot be constructed as a probability measure. In particular, the finite-dimensional truncated Gibbs measures have no weak limit in an appropriate space, even up to a subsequence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_17013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system Seong, Kihoon Probability Mathematical Physics Analysis of PDEs We study singular Gibbs measures for the three-dimensional Schrödinger-wave system, also known as the Yukawa system. Our primary result is the phase transition between weak and strong coupling cases, a phenomenon absent in one- and two-dimensional cases. Therefore, the three-dimensional model turns out to be critical, exhibiting the phase transition. In the weak coupling case, the Gibbs measure can be normalized as a probability measure and is shown to be singular with respect to the Gaussian free field. Conversely, in the strong coupling case, the Gibbs measure cannot be constructed as a probability measure. In particular, the finite-dimensional truncated Gibbs measures have no weak limit in an appropriate space, even up to a subsequence. |
| title | Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2306.17013 |