The Renormalization Group According to Balaban - I. Small fields
J. Dimock
TL;DR
This paper provides an expository overview of Balaban's renormalization group approach, illustrating it through the ultraviolet problem for scalar phi^4 theory on a 3D lattice, focusing on small field contributions.
Contribution
It offers a detailed explanation of Balaban's method and presents a new proof of the stability bound for the scalar phi^4 model.
Findings
Analysis of small field contribution to the partition function
New proof of the stability bound for phi^4 model
Illustration of the renormalization group approach
Abstract
This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the the ultraviolet problem for the scalar phi^4 model on a toroidal lattice in dimension d=3. This yields another proof of the stability bound. In this first paper we analyze the small field contribution to the partition function.
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