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

J. J. Godina·Y. Meurice·M. B. Oktay
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Abstract

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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J. J. Godina, Y. Meurice, M. B. Oktay. 1998-10-16. High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model. https://doi.org/10.1103/physrevd.59.096002

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