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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.19176 |
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| _version_ | 1866912601659670528 |
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| author | Chatterjee, Sourav Yakir, Oren |
| author_facet | Chatterjee, Sourav Yakir, Oren |
| contents | We study the lattice Yang-Mills-Higgs model with inverse gauge coupling $β>0$ and Higgs length $α>0$, in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2$ and (abelian) gauge group U(1), we prove that for any $m>0$, if $α= mβ$ and $β$ is large enough, the model exhibits exponential decay of correlations. This extends the classical result of Osterwalder and Seiler (1978), who required in addition that $m$ be sufficiently large. Our result also verifies a phase diagram from the physics literature, predicted by Fradkin and Shenker (1979). The proof is based on the Glimm-Jaffe-Spencer cluster expansion around a massive Gaussian field, following the approach of Balaban et al. (1984). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Correlation decay for U(1) lattice Higgs theory: the case of small mass Chatterjee, Sourav Yakir, Oren Probability Mathematical Physics We study the lattice Yang-Mills-Higgs model with inverse gauge coupling $β>0$ and Higgs length $α>0$, in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2$ and (abelian) gauge group U(1), we prove that for any $m>0$, if $α= mβ$ and $β$ is large enough, the model exhibits exponential decay of correlations. This extends the classical result of Osterwalder and Seiler (1978), who required in addition that $m$ be sufficiently large. Our result also verifies a phase diagram from the physics literature, predicted by Fradkin and Shenker (1979). The proof is based on the Glimm-Jaffe-Spencer cluster expansion around a massive Gaussian field, following the approach of Balaban et al. (1984). |
| title | Correlation decay for U(1) lattice Higgs theory: the case of small mass |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2509.19176 |