ABSTRACT
Wilson (1974) studied this question using a linear RG
applied to a Gaussian model. Let us sketch some of their
basic ideas.
If there are many fixed points other than the ones
we are looking for, we may get a wrong fixed point because
we cannot distinguish it from the right one with just a small
number of spins. For example, there are fixed points
which have an infinite range of interaction among spins,
although such fixed points cannot be reached i f we apply the
RG to a Hamiltonian with short-range (i. e. , finite) in terac-
tions. The fixed points of interest are those with short-
range interactions. The exact range of a short-range
fixed point depends on the detailed definition of the RG.
