Skip to ContentSkip to Navigation
About us Latest news News News articles

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

10 February 2012

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.
Share this Facebook LinkedIn
View this page in: Nederlands

More news

  • 03 April 2025

    IMChip and MimeCure in top 10 of the national Academic Startup Competition

    Prof. Tamalika Banerjee’s startup IMChip and Prof. Erik Frijlink and Dr. Luke van der Koog’s startup MimeCure have made it into the top 10 of the national Academic Startup Competition.

  • 01 April 2025

    NSC’s electoral reform plan may have unwanted consequences

    The new voting system, proposed by minister Uitermark, could jeopardize the fundamental principle of proportional representation, says Davide Grossi, Professor of Collective Decision Making and Computation at the University of Groningen

  • 01 April 2025

    'Diversity leads to better science'

    In addition to her biological research on ageing, Hannah Dugdale also studies disparities relating to diversity in science. Thanks to the latter, she is one of the two 2024 laureates of the Athena Award, an NWO prize for successful and inspiring...