Rethinking Dimensional Regularization in Critical Phenomena

P. Beretta; A. Codello

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arXiv · 2604.25103

Rethinking Dimensional Regularization in Critical Phenomena

P. Beretta·A. Codello

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Abstract

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.

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P. Beretta, A. Codello. 2026-04-28. Rethinking Dimensional Regularization in Critical Phenomena. https://arxiv.org/abs/2604.25103

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