  A study of the renormalization group flow in the three-dimensional nonlinear
O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is
presented. To achieve this, we combine an improved blockspin transformation
with the canonical demon method to determine the flow diagram for a number of
different truncations. Systematic errors of the approach are highlighted.
Results are discussed with hindsight on the fixed point structure of the model
and the corresponding critical exponents. Special emphasis is drawn on the
existence of a nontrivial ultraviolet fixed point as required for theories
modeling the asymptotic safety scenario of quantum gravity.
