vix.ing · top · new · best · stats · spec

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

1996/08/06 by Y. Meurice, S. Niermann, G. Ordaz · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #cond-mat #hep-lat #hep-th

paper · pdf · doi:10.1007/bf02181492

21 pages, 10 Postcript figures, latex file, uses revtex

arxiv created 1996/08/06 · openalex publication_date 1997/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 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.

Cited by