High-accuracy calculations of the critical exponents of Dyson’s hierarchical model

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 $\gamma =1.299140730159\mathrm{}\pm {10}^{-12}$. 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.