[SoSe 2024] Gibbs measures in statistical mechanics

Regular time: Thursday, 14:15--15:45, Room: MAR 4.064

The first meeting will take place on Thursday, 18.04.2024  at 14:15.


In this seminar, we will explore several topics related to Gibbs measures in statistical mechanics, from the classical results of D. Ruelle and R.L. Dobrushin in the ‘60s to the state of the art in Gibbs point process theory.

After the seminar, interested students will also be able to ask Professor W. König and me for a Bachelor’s/Master’s thesis.

Possible topics are, for example:

  1. The Ising model: finite-volume Gibbs measures and the consistency problem
  2. Infinite-volume Gibbs measures on the lattice: DLR equations
  3. Gibbs measures in the continuum: existence for finite-range interactions
  4. The Gibbs variational principle for finite-range interactions
  5. Phase transitions: the Widom—Rowlinson model
Additional topics may be selected at the choice of the students. The above are mostly taken from the following references.

Books and lecture notes:

[1] Statistical mechanics of lattice systems (2017) S. Friedli, I. Velenik

[2] Gibbs measures and phase transitions (2011) H.O. Georgii

[3] Introduction to the theory of Gibbs point processes (2019) D. Dereudre

[4] Lectures on the Poisson Process (2017) G. Last, M. Penrose

Papers:

[5] Variational principle for Gibbs point processes with finite range interaction (2016) D. Dereudre

[6] The analysis of the Widom—Rowlinson model by stochastic geometric methods (1995) J.T. Chayes, L. Chayes, R. Kotecký