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On the renormalization group iteration of a two-dimensional hierarchical nonlinear O(N) \(\sigma\)-model. (English) Zbl 0734.58052

Summary: We investigate the behaviour of a simplified two-dimensional non-linear O(N) \(\sigma\)-model under Wilson renormalization group transformations in the small coupling region. It can be controlled rigorously by suitable bounds on polymer activities uniformly for all field configurations, i.e. there is no need for a separate discussion of large and small field domains. This investigation provides us some preliminary insights to the renormalization group flow of and to phase space expansion methods applied to the complete \(\sigma\)-model.

MSC:

58Z05 Applications of global analysis to the sciences
81T10 Model quantum field theories
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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