The Renormalization Group According to Balaban - I. Small fields

J. Dimock

Published 2011-08-05, updated 2012-12-21Version 2

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.