[R. Kotecky] [CTS][seminars]

Prague Phase Transitions

A three-week Graduate Course on various topics in Mathematical
Statistical Physics will be held in Prague, for the second time. Each lecturer
will present a series of 2--3 talks, on __Mathematics and Physics of Phase
Transitions__, accessible for graduate, post-doc, as well as advanced
undergraduate students.

The lectures will take place at the Center for Theoretical Study and the Faculty of Mathematics and Physics, Charles University. In addition to 2 two-hour lectures each day, talks and seminars by post-docs and students are planned. Some additional informal activities in Prague and its surroundings will be organized in the remaining time.

**The Course starts on April 6 and runs until April 24.
**

Each lecturer is going to present a minicourse consisting of up to 3 talks (a talk is be default something between 3/2-2 hours).

The tentative program:

**April 6--9 **[detailed
programm]

**C. Borgs:** First order transitions and finite-size
scaling

**J. T. Chayes: **Percolation and the Random Cluster
Model

[A course on percolation ps file]

**J.-D. Deuschel: **Some Aspects of Continuous Gradient
Systems

[Abstract]

**April 14--17 **[detailed
programm]

**G. Ben-Arous: **Spin Glasses: Statics and Dynamics

**C. Gruber: **Grassmann algebras and applications
to itinerant electrons

**F. den Hollander: **Probabilistic models for polymer
chains

**Y. Velenik: **Macroscopic description of phase separation.**
**

Abstract: Thermodynamics states that the macroscopic geometry of a system in the phase separation regime can be obtained through a minimization of the total surface free energy. We discuss how this variational problem can be derived from the first principles of statistical mechanics in the case of the 2D Ising model.

Reference: Some relevant papers can be found at the address Velenik in the section research.

**April 20--24 **[detailed
programm]

**F. Dunlop: **Cluster Expansions around the Gaussian
Capillary Waves Model

[Abstract]

**C. Maes: **Many-particle systems with unbounded interactions**
**

A short overview of the standard Gibbsian set-up and standard Glauber dynamics. Indication how non-Gibbsian measures can arise. Discussion of concepts like almost Gibbsian and weakly Gibbsian measures. The picture, as of today, for the Dobrushin program on Gibbsian restorations. Dynamical analogues with an application to sandpiles. Relation with random unbounded interactions.

References : 1. van Enter, Fernandez, Sokal: "the thick paper", 2. paper by Maes, Redig, van Moffaert in mp-arch

**C. Kuelske:** Metastates and
Chaotic size dependence in random systems

In disordered systems the large volume behavior of the finite volume Gibbs-measures with fixed realization of the disorder can be complicated in the presence of phase transitions. Some concepts to describe the asymptotic behavior in these cases are discussed and illustrated in mean-field type examples.

References: 1. Newman, C.M.: Topics in Disordered Systems, Lectures in Mathematics, ETH Zurich, Birkh\"auser (1997), 2. C. Kuelske: Metastates in Disordered Mean Field Models: Random Field and Hopfield Models, J.Stat.Phys 88 Issue 5/6 (1997)

**O. Hryniv: **One-dimensional polymer models: some
limit results

1D polymer models arise naturally in many areas of mathematics, from combinatorics and number theory to probability theory and statistical mechanics. We discuss some general approaches to investigating such models and apply them to study the surface tension in 2D contour models (Ising, SAW etc).

References: 1. Graham, R.L.(ed.); Groetschel, Martin (ed.); Lovasz, Laszlo (ed.) Handbook of combinatorics. Vol. 1-2. Amsterdam: Elsevier (North-Holland), (1995). 2. Dobrushin, R.; Kotecky, R.; Shlosman, S. Wulff construction. A global shape from local interaction. Translations of Mathematical Monographs. 104. Providence, RI: AMS (1992). 3. R. Dobrushin , O. Hryniv: Fluctuations of the Phase Boundary in the 2D Ising Ferromagnet Comm Math Phys 189 (1997) 2, 395-445 and ESI preprint (no. 355)

**W.A. Majewski: **Quantum chaos

Unfortunately, no financial subsistence can be provided this time, except in exceptional cases (some very limited resources are available from a local grant). However, living expenses for the duration of the entire Course will be less than 600 $ (lodging will be available for about 100 $ per week, additional living costs are less than 100 $ per week).

Students interested please sign up via e-mail on the address:

Here is a page concerning the accomodation of the participants.

Last updated April 2, 1998