Sharp phase transition in the grand canonical $Φ^3$ measure at critical chemical potential
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912532879376384 |
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| author | Barashkov, Nikolay Seong, Kihoon Sosoe, Philippe |
| author_facet | Barashkov, Nikolay Seong, Kihoon Sosoe, Philippe |
| contents | We study the phase transition and critical phenomenon for the grand canonical $Φ^3$ measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen--Fröhlich--Lebowitz, primarily in regimes far from criticality. We identify a critical chemical potential and show that the measure exhibits a sharp phase transition at this critical threshold. At the critical threshold, the analysis is based on establishing the correlation decay of the Gaussian fluctuations in the partition function, combined with a coarse-graining argument to show divergence of the maximum of an approximating Gaussian process. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_08427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp phase transition in the grand canonical $Φ^3$ measure at critical chemical potential Barashkov, Nikolay Seong, Kihoon Sosoe, Philippe Probability Mathematical Physics Analysis of PDEs 81T08, 82B26, 82B27, 60H30 We study the phase transition and critical phenomenon for the grand canonical $Φ^3$ measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen--Fröhlich--Lebowitz, primarily in regimes far from criticality. We identify a critical chemical potential and show that the measure exhibits a sharp phase transition at this critical threshold. At the critical threshold, the analysis is based on establishing the correlation decay of the Gaussian fluctuations in the partition function, combined with a coarse-graining argument to show divergence of the maximum of an approximating Gaussian process. |
| title | Sharp phase transition in the grand canonical $Φ^3$ measure at critical chemical potential |
| topic | Probability Mathematical Physics Analysis of PDEs 81T08, 82B26, 82B27, 60H30 |
| url | https://arxiv.org/abs/2508.08427 |