Aernout van Enter

"Evolving Gibbs measures, Gibbs or not?"

Abstract: When  a Gibbs measure is subjected to an evolution of Glauber type, to describe a fast changing of temperature for example, one can wonder if at the intermediate times , between being at the initial and final temperatures, one is at some intermediate temperature. Here the effective temperature would be  given by the inverse of some interaction norm for which the evolved state is a Gibbs measure.
We show a number of results, both for discrete- and continuous-spin models, in which the evolved state may either be or not be a Gibbs measure.
We derive this by giving a space-time picture, in which the Gibbs-nonGibbs question is interpreted as the absence or presence of a phase transition between having different histories under conditioning.