Global Renormalization Group

TL;DR

This paper discusses the application of the renormalization group to complex systems with multiple scaling regimes, exemplified by the four-dimensional  model near spinodal instability, revealing an amplification mechanism for high-energy forces.

Contribution

It introduces a novel approach to applying the renormalization group to systems with multiple scaling regimes, using the  model as an example, and highlights the amplification mechanism near spinodal instability.

Findings

Identification of a nontrivial low energy scaling regime near spinodal instability

Proposal of an effective theory that amplifies signals for nonuniversal forces

Potential to explore high-energy forces through the amplification mechanism

Abstract

The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is identified in the vicinity of the spinodal instability region. It is pointed out that the effective theory defined in the vicinity of the spinodal instability offers an amplification mechanism, a precursor of the condensation that can be used to explore nonuniversal forces at high energies.