  We report an essential improvement of the plain Fourier Monte Carlo algorithm
that promises to be a powerful tool for investigating critical behavior in a
large class of lattice models, in particular those containing microscopic or
effective long-ranged interactions. On tuning the Monte Carlo acceptance rates
separately for each wave vector, we are able to drastically reduce critical
slowing down. We illustrate the resulting efficiency and unprecedented accuracy
of our algorithm with a calculation of the universal elastic properties of
crystalline membranes in the flat phase and derive a numerical estimate eta =
0.795(10) for the critical exponent eta that challenges those derived from
other recent simulations. The large system sizes accessible to our present
algorithm also allow to demonstrate that insufficiently taking into account
corrections to scaling may severely hamper a finite size scaling analysis. This
observation may also help to clarify the apparent disagreement of published
numerical estimates of eta in the existing literature.
