Is the fuzzy Potts model Gibbsian?

Is the Fuzzy Potts Model Gibbsian?

– The fuzzy Potts model is obtained by looking at the Potts model with a pair of glasses that prevents distinguishing between some of the spin values. We show that the fuzzy Potts model on Z (d 2) is Gibbsian at high temperatures and non-Gibbsian at low temperatures.  2003 Published by Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Le modèle de Potts flou est obtenu en regardant le...

Is the fuzzy Potts model Gibbsian?

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 m...

Translation-invariance of two-dimensional Gibbsian systems of particles with internal degrees of freedom

The conservation of translational symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian systems of marked particles with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interactions are included. In particular we thus show the conservation of translational symm...

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 mor...