The Renormalization Group According to Balaban, I. The Small Fields

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Referee this paper: [arXiv:1108.1335] by J. Dimock

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Balaban has developed a very powerful renormalization group method for analyzing lattice quantum field theories. This paper by J. Dimock is the first of three giving an expository account of Balaban's approach to the renormalization group, illustrating the method with a treatment of the the ultraviolet problem for the scalar $\Phi^4$ model on a toroidal lattice in dimension $d=3$.

This first part analyzes the small field contribution to the partition function. See also part II and part III.