Journal article
The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis
Journal of statistical physics, Vol.87(1), pp.363-383
08/06/1996
DOI: 10.1007/BF02181492
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
a 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 K.
Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma $ 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 $\epsilon $-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.
Details
- Title: Subtitle
- The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis
- Creators
- Y Meurice - University of IowaS Niermann - University of IowaG Ordaz - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of statistical physics, Vol.87(1), pp.363-383
- DOI
- 10.1007/BF02181492
- ISSN
- 0022-4715
- eISSN
- 1572-9613
- Language
- English
- Date published
- 08/06/1996
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984200024602771
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