The Small Field Parabolic Flow for Bosonic Many-body Models: Part 4 - Background and Critical Field Estimates

TL;DR

This paper develops bounds on background and critical fields in a weakly interacting bosonic lattice system, advancing the understanding of symmetry breaking via a parabolic flow analysis in the renormalization group framework.

Contribution

It provides rigorous bounds and existence proofs for background and critical fields within the small field approximation of the parabolic flow in bosonic many-body models.

Findings

Existence of background and critical fields established.

Bounds on these fields derived using steepest descent methods.

Supports the analysis of symmetry breaking in bosonic systems.

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. Here we prove the existence of and bounds on the background and critical fields that arise from the steepest descent attack that is at the core of our renormalization group step anaylsis of these models.