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.
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Meurice, Y., Niermann, S. & Ordaz, G. The oscillatory behavior of the high-temperature expansion of Dyson's hierarchical model: A renormalization group analysis. J Stat Phys 87, 363–383 (1997). https://doi.org/10.1007/BF02181492
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DOI: https://doi.org/10.1007/BF02181492