Aernout C.D. van Enter
Ill-defined block-spin transformations at arbitrarily high temperatures.
(22K, latex)

ABSTRACT.  Examples are presented of block-spin transformations
which map the Gibbs measures of the Ising model in two or more 
dimensions at temperature intervals extending to arbitrarily high
temperatures onto non-Gibbsian measures. In this way we provide the 
first example of this kind of pathology for very high temperatures,
and as a corollary also the first example of such a pathology happening
at a critical point.