Pathological Behavior of Renormalization-Group Maps at High Fields and   Above the Transition Temperature
  We show that decimation transformations applied to high-$q$ Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested. 
Aernout C. D. van Enter and Roberto Fern\'andez and Roman Koteck\'y