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• W3123295286 abstract "We consider an Euclidean supersymmetric field theory in ℤ3 given by a supersymmetric Φ4 perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green’s function of a (stable) Lévy random walk in ℤ3. The Green’s function depends on the Lévy-Khintchine parameter $alpha ={3+varepsilon over 2}$ with 0<α<2. For $alpha ={3over 2}$ the Φ4 interaction is marginal. We prove for $alpha -{3over 2}={varepsilon over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green’s function of a (weakly) self-avoiding Lévy walk in ℤ3 is a second moment (two point correlation function) of the supersymmetric measure governing this model. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding Lévy walk in ℤ3." @default.
• W3123295286 created "2021-02-01" @default.
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• W3123295286 date "2008-11-11" @default.
• W3123295286 modified "2023-10-14" @default.
• W3123295286 title "The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice ℤ3" @default.
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• W3123295286 doi "https://doi.org/10.1007/s10955-008-9626-8" @default.
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