Functional Dimensional Regularization for O(N) Models

TL;DR

The paper introduces a functional dimensional regularization scheme that efficiently computes critical exponents for the $O(N)$ universality class, matching results from advanced non-perturbative methods.

Contribution

It explicitly derives flow equations for the $O(N)$ class using FDR, demonstrating its effectiveness and rapid convergence compared to existing approaches.

Findings

FDR yields critical exponents comparable to higher-order non-perturbative methods.

FDR reproduces known results from the $ ext{epsilon}$-expansion for various universality classes.

FDR demonstrates efficiency and rapid convergence in computing critical exponents.

Abstract

The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the $\varepsilon$-expansion for the Ising and other universality classes. In this work, we show that this is not a mere coincidence: by applying the scheme to the $O(N)$ universality class, we explicitly derive the flow equations and obtain critical exponents that are comparable to those obtained with higher-order non-perturbative approaches. In this case, FDR retains the features already highlighted in previous works -- namely, its efficiency and rapid convergence.