Journal of Statistical Physics

, Volume 87, Issue 1–2, pp 363–383 | Cite as

The oscillatory behavior of the high-temperature expansion of Dyson's hierarchical model: A renormalization group analysis

  • Y. Meurice
  • S. Niermann
  • G. Ordaz
Articles

Abstract

We calculate 800 coefficients of the high-temperature expansion of the magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg measure. Log-periodic corrections to the scaling laws appear as in the case of an Ising measure. The period of oscillation appears to be a universal quantity given in good approximation by the logarithm of the largest eigenvalue of the linearized RG transformation, in agreement with a possibility suggested by Wilson and developed by Niemeijer and van Leeuwen. We estimate γ to be 1.300 (with a systematic error of the order of 0.002), in good agreement with the results obtained with other methods, such as the ε-expansion. We briefly discuss the relationship between the oscillations and the zeros of the partition function near the critical point in the complex temperature plane.

Key Words

Renormalization group critical exponents hierarchical models high-temperature expansion Ising models epsilon expansion 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Y. Meurice
    • 1
  • S. Niermann
    • 1
  • G. Ordaz
    • 1
  1. 1.Department of Physics and AstronomyUniversity of IowaIowa City

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