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Renormalization group approach to the hierarchical model

  • Section III
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Feynman Path Integrals

Part of the book series: Lecture Notes in Physics ((LNP,volume 106))

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Abstract

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.].

Work supported by the University of Geneva. 2

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References

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Authors and Affiliations

  1. Harvard University, 02138, Cambridge, Massachusetts, USA

    Pierre Collet

Authors
  1. Pierre Collet
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Editor information

S. Albeverio Ph. Combe R. Høegh-Krohn G. Rideau M. Sirugue-Collin M. Sirugue R. Stora

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© 1979 Springer-Verlag

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Collet, P. (1979). Renormalization group approach to the hierarchical model. In: Albeverio, S., et al. Feynman Path Integrals. Lecture Notes in Physics, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09532-2_71

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  • DOI: https://doi.org/10.1007/3-540-09532-2_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09532-3

  • Online ISBN: 978-3-540-35039-2

  • eBook Packages: Springer Book Archive

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