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The renormalization group according to Balaban. III: Convergence. (English) Zbl 1302.81139
Summary: 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.
For Part I see [the author, Rev. Math. Phys. 25, No. 7, Article ID 1330010, 64 p. (2013; Zbl 1275.81068)] and for Part II see [the author, J. Math. Phys. 54, No. 9, 092301, 85 p. (2013; Zbl 1284.81217)].

##### MSC:
 81T17 Renormalization group methods applied to problems in quantum field theory 81T10 Model quantum field theories 81T25 Quantum field theory on lattices 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
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##### References:
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