A Complete Renormalization Group Trajectory Between Two Fixed Points

TL;DR

This paper constructs a rigorous nonperturbative renormalization group trajectory in a 3D Euclidean field theory, connecting the Gaussian fixed point to the Wilson-Fisher fixed point, demonstrating a mean field to critical crossover.

Contribution

It provides the first rigorous nonperturbative construction of a renormalization group trajectory connecting two fixed points in a 3D field theory.

Findings

Successfully constructs a massless RG trajectory between fixed points.

Shows the crossover from mean field to Wilson-Fisher fixed point.

Advances understanding of nonperturbative RG flows in quantum field theory.

Abstract

We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson's exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.