Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

TL;DR

This paper demonstrates that certain renormalization-group transformations lead to non-Gibbsian measures in high-q Potts models and strong-field Ising models, indicating widespread pathological behavior beyond prior examples.

Contribution

It reveals that non-Gibbsian measures arise from decimation and majority transformations in models at high fields and temperatures, expanding understanding of RG transformation issues.

Findings

Decimation transformations cause non-Gibbsian measures in high-q Potts models above transition temperature.

Majority transformations produce non-Gibbsian measures in strong-field, low-temperature Ising models.

Pathological behavior of RG transformations is more common than previously thought.

Abstract

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.