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arXiv:2107.00466 · Physical Review Letters

Inverse Renormalization Group in Quantum Field Theory

Dimitrios Bachtis, Gert Aarts A, Francesco Di Renzo, Biagio Lucini A

Published Feb 23, 2022• 25 citations
arXivHTMLPDF

Abstract

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional ϕ^{4} scalar field theory on sizes as small as V=8^{2}, we apply the inverse transformations to produce rescaled systems of size up to V^{'}=512^{2} which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

DOI
10.1103/physrevlett.128.081603

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Abstract Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.