  We perform high-accuracy calculations of the critical exponent gamma and its
subleading exponent for the 3D O(N) Dyson's hierarchical model, for N up to 20.
We calculate the critical temperatures for the nonlinear sigma model measure.
We discuss the possibility of extracting the first coefficients of the 1/N
expansion from our numerical data. We show that the leading and subleading
exponents agreewith Polchinski equation and the equivalent Litim equation, in
the local potential approximation, with at least 4 significant digits.
