Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-08-06
Physics
High Energy Physics
High Energy Physics - Lattice
21 pages, 10 Postcript figures, latex file, uses revtex
Scientific paper
10.1007/BF02181492
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.
Meurice Yannick
Niermann S.
Ordaz G.
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