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.
Last modified: | 13 March 2020 12.59 a.m. |
More news
-
02 July 2024
Start EngD programmes Autonomous Systems and Sustainable Process Design
In September, the Engineering Doctorate (EngD) programmes Autonomous Systems and Sustainable Process Design will start at the Faculty of Scfience and Engineering.
-
25 June 2024
Heineken Young Scientists Award for Casper van der Kooi
For his research in the field of Natural Sciences, Casper van der Kooi will receive the Heineken Young Scientists Award.
-
24 June 2024
Measuring stickiness
Several plant species use tiny sticky droplets to attract and trap insects. These droplets form an ideal toxin-free insecticide that could be easily washed off of edible plants. Abinaya Arunachalam built a tool to measure the stickiness of...