The Small Field Parabolic Flow for Bosonic Many-body Models: Part 3 - Nonperturbatively Small Errors

TL;DR

This paper investigates the parabolic flow in weakly interacting bosonic systems, providing arguments that the small field approximation closely matches the full model with nonperturbatively small errors, advancing understanding of symmetry breaking.

Contribution

It offers nonperturbative estimates showing the small field approximation is very close to the full model in bosonic many-body systems.

Findings

Small field approximation differs from the full model by nonperturbatively small errors.

Supports the validity of the parabolic flow approach in analyzing symmetry breaking.

Provides theoretical arguments rather than complete proofs.

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 "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we provide arguments that suggest, but do not completey prove, that the difference between the "small field" approximation and the full model is nonperturbatively small.