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

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.