Year: 2021
Type: article
Abstract: Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non- perturbative characterization, and this is what is presented here in a model of symplectic fermions with a nonlocal (“long-range”) kinetic term depending on a parameterεand a quartic interaction. We identify the Banach space of interactions, which the fixed point belongs to, and we determine it via a convergent approximation scheme. The Banach space is not limited to relevant interactions, but it contains all possible irrelevant terms with short-ranged kernels, decaying like a stretched exponential at large distances. As the model shares a number of features in common withϕ4or Ising models, the result can be used as a benchmark to test the validity of truncations and approximations in RG studies. The analysis is based on results coming from Constructive RG to which we provide a tutorial and self-contained introduction. In addition, we prove that the fixed point is analytic inε, a somewhat surprising fact relying on the fermionic nature of the problem.
Source: Journal of High Energy Physics
Authors: Alessandro Giuliani, Vieri Mastropietro, Slava Rychkov
Institutions: Roma Tre University, Accademia Nazionale dei Lincei, University of Milan, Centre National de la Recherche Scientifique, Université Paris Cité, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Laboratoire de Physique de l'Ecole Normale Supérieure, Institut des Hautes Études Scientifiques
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3048906996