Rethinking Dimensional Regularization in Critical Phenomena
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910172815818752 |
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| author | Beretta, P. Codello, A. |
| author_facet | Beretta, P. Codello, A. |
| contents | We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rethinking Dimensional Regularization in Critical Phenomena Beretta, P. Codello, A. High Energy Physics - Theory Statistical Mechanics Mathematical Physics We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs. |
| title | Rethinking Dimensional Regularization in Critical Phenomena |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2604.25103 |