We discuss a recently introduced real space renormalization group (RSR
G) approach. Unlike other RSRGs, it does not depend upon weight functi
ons arisen from particular recipes like majority rule or others. Inste
ad, it is formulated assuming only the validity of Fisher's finite siz
e scaling hypothesis. Because.of this, it is free from conceptual crit
icisms normally invoked against RSRGs, as well as other unpleasant con
sequences of particular weight function choices as the so-called proli
feration of parameters, for instance. Simple exact calculations can be
performed for small lattice sizes, yielding qualitative informations
and reasonably accurate quantitative critical frontiers and exponents.
Very accurate values can be obtained, however, performing the same ca
lculations for larger lattices, using Monte Carlo sampling.