Abstract
In this paper, the Hierarchical Model is studied near a non-trivial fixed point φɛ of its renormalization group. Our analysis is an extension of work of Bleher and Sinai. We prove the validity of the ɛ-expansion for φɛ. We then show that the renormalization transformations around φɛ have an unstable manifold which is completely characterized by the tangent map and can be brought to normal form. We then establish relations between this result and the critical behaviour of the model in the thermodynamic limit.
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Collet, P., Eckmann, J.P. The ɛ-expansion for the Hierarchical Model. Commun.Math. Phys. 55, 67–96 (1977). https://doi.org/10.1007/BF01613151
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DOI: https://doi.org/10.1007/BF01613151