High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

Details High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

1998-10-16

arxiv.org/abs/hep-lat/9810034v1

Phys.Rev. D59 (1999) 096002

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, 9 figures, uses revtex

Scientific paper

10.1103/PhysRevD.59.096002

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.

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