Abstract
It is shown that the Migdal approximate-renormalization recursion formulas always bring the initial state into the high-temperature region for the U(1)-invariant models at the critical dimensions. This means that the Migdal recursion formulas fail to exhibit the Kosterlitz-Thouless transitions. This is also the case for the recursion formulas of Kadanoff type. The method developed here is extended to non-Abelian systems by some additional tricks.