The Renormalization Group According to Balaban - III. Convergence

TL;DR

This paper explains Balaban's renormalization group method, demonstrating the convergence of the expansion and establishing a stability bound for the scalar phi^4 model on a 3D lattice.

Contribution

It provides a detailed exposition of Balaban's approach, completing the proof of convergence and stability for the scalar phi^4 model.

Findings

Proved convergence of the renormalization group expansion.

Established a stability bound for the scalar phi^4 model.

Illustrated the method with the ultraviolet problem in three dimensions.

Abstract

This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the ultraviolet problem for the scalar phi^4 model on a toroidal lattice in dimension d=3. In this third paper we demonstrate convergence of the expansion and complete the proof of a stability bound.