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.