Inverse Renormalization Group in Quantum Field Theory

TL;DR

This paper introduces inverse renormalization group transformations in quantum field theory to efficiently analyze critical phenomena, enabling rescaling of small configurations to larger systems and extracting critical exponents.

Contribution

It presents a novel inverse RG method that produces critical fixed points and inverse flows, improving analysis of critical systems in quantum field theory.

Findings

Successfully rescaled small configurations to larger systems up to 512^2

Extracted two critical exponents from the rescaled systems

Demonstrated the method's applicability to various configuration-generating techniques

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 $\phi^{4}$ 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.