  Effective Boltzmannians in the sense of the block spin renormalization group
are computed for the 2D Ising model. The blocking is done with majority and
Kadanoff rules for blocks of size 2 by 2. Transfer matrix techniques allow the
determination of the effective Boltzmannians as polynomials in u=exp(4 Beta)
for lattices of up to 4 by 4 blocks. The zeroes of these polynomials are
computed for all non-equivalent block spin configurations. Their distribution
in the complex Beta plane reflects the regularity structure of the block spin
transformation. In the case of the Kadanoff rule spurious zeroes approach the
positive real Beta axis at large values of Beta. They might be related to the
renormalization group pathologies discussed in the literature.
