Renormalization group trajectories between two fixed points

TL;DR

This paper rigorously constructs complete renormalization group trajectories connecting two fixed points in a three-dimensional phi-four model, advancing nonperturbative understanding of critical phenomena.

Contribution

It provides a rigorous, nonperturbative construction of RG trajectories between fixed points without hierarchical approximation, using a fixed point approach in Banach space.

Findings

Constructed RG trajectories connecting UV and IR fixed points.

Established nonperturbative, rigorous RG map for the phi-four model.

Demonstrated trajectories via fixed point in Banach space.

Abstract

We report on our recent rigorous construction of complete renormalization group trajectories between two fixed points for the three-dimensional phi-four model with modified propagator considered by Brydges, Mitter and Scoppola (BMS). These are discrete critical trajectories which connect the ultraviolet Gaussian fixed point to the nontrivial BMS infrared fixed point which is an analogue of the Wilson--Fisher fixed point. The renormalization group map is defined rigorously and nonperturbatively, without using the hierarchical approximation. The trajectories are constructed by a fixed point argument in a suitable Banach space of sequences, where one perturbs a nonlinear one-dimensional iteration.