  The computation of the critical exponent eta characterizing the universal
elastic behavior of crystalline membranes in the flat phase continues to
represent challenges to theorists as well as computer simulators that manifest
themselves in a considerable spread of numerical results for eta published in
the literature. We present new insight to this problem that results from
combining Wilson's momentum shell renormalization group method with the power
of modern computer simulations based on the Fourier Monte Carlo algorithm.
After discussing the ideas and difficulties underlying this combined scheme, we
present a calculation of the renormalization group flow of the effective 2d
Young modulus for momentum shells of different thickness. Extrapolation to
infinite shell thickness allows to produce results in reasonable agreement with
those obtained by functional renormalization group or by Fourier Monte Carlo
simulations in combination with finite size scaling. Moreover, our new method
allows for the first time to obtain a decent estimate for the value of the
Wegner exponent omega that determines the leading correction to scaling, which
in turn allows to refine our numerical estimate for eta previously obtained
from precise finite size scaling data.
