  We investigate finite lattice approximations to the Wilson Renormalization
Group in models of unconstrained spins. We discuss first the properties of the
Renormalization Group Transformation (RGT) that control the accuracy of this
type of approximations and explain different methods and techniques to
practically identify them. We also discuss how to determine the anomalous
dimension of the field. We apply our considerations to a linear sigma model in
two dimensions in the domain of attraction of the Ising Fixed Point using a
Bell-Wilson RGT. We are able to identify optimal RGTs which allow accurate
computations of quantities such as critical exponents, fixed point couplings
and eigenvectors with modest statistics. We finally discuss the advantages and
limitations of this type of approach.
