Journal Article

FZJ-2020-04068

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Momentum-dependence in the infinitesimal Wilsonian renormalization group

Helias, M. (Corresponding author)FZJ*

2020
IOP Publ. Bristol

This record in other databases:  

Please use a persistent id in citations: http://hdl.handle.net/2128/25921  doi:10.1088/1751-8121/abb169

Abstract: Wilson's original formulation of the renormalization group is perturbative in nature. We here present an alternative derivation of the infinitesimal momentum shell renormalization group, akin to the Wegner and Houghton scheme, that is a priori exact. We show that the momentum-dependence of vertices is key to obtain a diagrammatic framework that has the same one-loop structure as the vertex expansion of the Wetterich equation. Momentum dependence leads to a delayed functional differential equation in the cutoff parameter. Approximations are then made at two points: truncation of the vertex expansion and approximating the functional form of the momentum dependence by a momentum-scale expansion. We exemplify the method on the scalar phiv4-theory, computing analytically the Wilson–Fisher fixed point, its anomalous dimension η(d) and the critical exponent ν(d) non-perturbatively in d ∈ [3, 4] dimensions. The results are in reasonable agreement with the known values, despite the simplicity of the method.

---

Contributing Institute(s):

1. Computational and Systems Neuroscience (INM-6)

Research Program(s):

1. 574 - Theory, modelling and simulation (POF3-574) (POF3-574)
2. HBP SGA2 - Human Brain Project Specific Grant Agreement 2 (785907) (785907)
3. neuroIC002 - Recurrence and stochasticity for neuro-inspired computation (EXS-SF-neuroIC002) (EXS-SF-neuroIC002)
4. RenormalizedFlows - Transparent Deep Learning with Renormalized Flows (BMBF-01IS19077A) (BMBF-01IS19077A)

Appears in the scientific report 2020

---

Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

---