Operators for Parabolic Block Spin Transformations

TL;DR

This paper develops bounds on operators involved in the renormalization group analysis of a weakly interacting Boson system, aiding the understanding of symmetry breaking and phase transitions in three-dimensional lattice models.

Contribution

It provides rigorous bounds on fluctuation integral covariance and linear operators within the parabolic flow analysis of Boson systems.

Findings

Bounds on fluctuation integral covariance are established.

Analysis supports the understanding of symmetry breaking in Boson systems.

Contributes to the mathematical foundation of renormalization group methods.

Abstract

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Bounds on the fluctuation integral covariance, as well as on some other linear operators, are an important ingredient in our renormalization group step analysis. These bounds are proven here.