Transformations of Gibbs States

It is known that simple renormalization transformation of Gibbs measures (states) can produce non-Gibssian measures. The hypothesis about the necessary and sufficient conditions for preservation of Gibbsianity - the so-called absence of the hidden phase-transitions, was proposed in 1993. I will discuss a novel interpretation of the hidden phase-transition scenario and some recent progress towards the proof. In the second part of the talk, I will discuss certain aspects of the Dobrushin reconstruction program for the renormalized Gibbs states (which may or may not be Gibbs). In particular, I will show that a generalized variational principle holds.