Euclidean scalar field theory in the bi-local approximation

TL;DR

This paper investigates the impact of bi-local saddle point contributions on the renormalization group blocking process in a 3D Euclidean phi^6 model, revealing new phases and restricting universality classes.

Contribution

It introduces the inclusion of bi-local saddle points in the RG blocking step, showing their effects on phase structure and universality classes in a scalar field theory.

Findings

Discovery of new phases due to bi-local effects

Restriction of certain universality classes

Alteration of phase structure in the phi^6 model

Abstract

The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bi-local saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean $\phi^6$ model in this work. The phase structure is changed, new phases and relevant operators are found and certain universality classes are restricted by the bi-local saddle point.