Functional Dimensional Regularization for O(N) Models
TLDR
This paper applies Functional Dimensional Regularization (FDR) to O(N) models, deriving flow equations and competitive critical exponents.
Key contributions
- Applies Functional Dimensional Regularization (FDR) to the O(N) universality class.
- Explicitly derives flow equations for O(N) models using the FDR scheme.
- Obtains critical exponents comparable to higher-order non-perturbative approaches.
- Demonstrates FDR's efficiency and rapid convergence for these complex systems.
Why it matters
This paper validates the novel Functional Dimensional Regularization (FDR) scheme by applying it to O(N) models. It shows FDR's capability to derive competitive critical exponents efficiently, offering a powerful alternative to existing complex methods.
Original 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.
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