A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $|φ|^4$ Models in $d \ge 4$ at and Above the Critical Point
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908634992082944 |
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| author | Park, Jiwoon |
| author_facet | Park, Jiwoon |
| contents | In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled $n$-component $|φ|^4$ model under periodic boundary conditions in dimension $d \ge 4$. Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at $d=4$. This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $|φ|^4$ Models in $d \ge 4$ at and Above the Critical Point Park, Jiwoon Probability Mathematical Physics In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled $n$-component $|φ|^4$ model under periodic boundary conditions in dimension $d \ge 4$. Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at $d=4$. This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions. |
| title | A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $|φ|^4$ Models in $d \ge 4$ at and Above the Critical Point |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2511.03495 |