Is an imaginary fixed point physical or unphysical?

TL;DR

This paper investigates whether an imaginary fixed point in a $\

Contribution

It demonstrates that the imaginary fixed point in the $\

Findings

Imaginary fixed points are physically meaningful.

Scaling behavior is governed by the imaginary fixed point.

Divergence of the RG flow occurs at a finite scale.

Abstract

It has been proposed that a first-order phase transition driven to happen in the metastable region exhibits scaling and universality near an instability point controlled by an instability fixed point of a $\varphi^3$ theory. However, this fixed point has an imaginary value and the renormalization-group flow of the $\varphi^3$ coupling diverges at a finite scale. Here combining a momentum-space RG analysis and a nucleation theory near the spinodal point, we show that imaginary rather than real values are physical counter-intuitively and thus the imaginary fixed point does control the scaling.