Metastates, non-Gibbsianness and phase transitions: a stroll through statistical mechanics

PhD ceremony: Mr. G. Iacobelli, 16.15 uur, Aula Academiegebouw, Broerstraat 5, Groningen

Dissertation: Metastates, non-Gibbsianness and phase transitions: a stroll through statistical mechanics

Promotor(s): prof. A.C.D. van Enter, prof. C. Külske

Faculty: Mathematics and Natural Sciences

In this thesis we present three works of a statistical mechanics avour. The concept of a Gibbs measure is primal in all of them.

The climax of the Gibbsian description of an infinite system is the possibility that several Gibbs measures exist for the same prescribed local laws. This accounts for the physical phenomenon of phase transitions. Another feature of the Gibbsian description, is the continuity of the conditional probabilities as a function of the conditioning, which relates to the physical concept of locality. In Chapter 4, we provide an example of how such a continuity can be lost if the system is subjected to a dynamics. More precisely, we show that under an infinite-temperature Glauber dynamics the homogeneous Ising Gibbs 1 measures on a Cayley tree lose the continuity, in a state-dependent manner, if we let the system evolve for sufficiently long time. In Chapter 5, we study phase transition for the Potts model with invisible colours on Z2. We prove that a first-order phase transition occurs if the number of invisible colours is large enough. In Chapter 3, we studied disordered meanfield models where both spin variables and disorder variables take finitely many values. We provide the construction of the metastate and we compute the probability weights which give us the appearance of the candidate states.