Renormalization group approach to the hierarchical model

  • Pierre Collet
Section III
Part of the Lecture Notes in Physics book series (LNP, volume 106)


The Hierarchical Model is a one dimensional ferromagnetic spin model with long range forces . Using the invariance of this model under a suitable renormalization group , we analyse the temperature behavior of the system . In particular , we prove the existence of a non-trivial fixed point and compute its critical indices using a local linearization of the renormalization transformation around the fixed point . Some global results ( cross-over ) are also described , and they provide a description of the phases near the critical point . This talk summarizes some of the results of joint work with J-P.Eckmann [C.E.].


Renormalization Group Hierarchical Model Unstable Manifold Stable Manifold Critical Index 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Pierre Collet
    • 1
  1. 1.Harvard UniversityCambridgeUSA

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