Pathological Behavior of Renormalization-group Maps at High Fields and above the Transition Temperature Contents 1 Introduction 1 2 Basic Set-up 2 3 Non-gibbsianness for Majority-rule Maps of Ising Models at High Magnetic Field 4

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 eld 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 .