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.
You can vote until October 5.
Dean Knoester leaves Groningen science faculty January 1, 2022
The grant of EUR 921,000 is for his project ‘Multi-scale assessment of liquid metal embrittlement at steel-zinc interfaces (MUSCLES).
The UG website uses functional and anonymous analytics cookies. Please answer the question of whether or not you want to accept other cookies (such as tracking cookies).
If no choice is made, only basic cookies will be stored. More information