MARK KAC SEMINAR
|The seminar of 2003-2004:||
Main speaker 2003-2004:
(Institute of Analysis and Scientific Computing, School of Mathematics, EPF-L, CH-1015 Lausanne)
first theory of condensation originated with the celebrated equation of state
of van der Waals.
complemented with the Maxwell Construction (``equal area rule'') it leads
to isotherms describing general characteristics of the liquid-vapor equilibrium.
The isotherms obtained with the van der Waals-Maxwell Theory have
a very simple analytic structure: they are analytic in a pure phase and have
analytic continuations along the liquid and gas branches, through the transition
points. These analytic continuations were originally interpreted as
describing the pressure of metastable states.
first lecture will be devoted to the history of the problem,
to a precise
formulation of the results, as well as an exposition of Pirogov-Sinai Theory,
which is the framework in which they are established.
second lecture will be devoted to a detailed
proof of Isakov's theorem and
its generalization .
In the last lecture the results concerning the Kac limit γ to 0 will be presented . I shall conclude with a discussion of important open problems.
Friedli S., Pfister C.-E., On the Singularity of the Free Energy at
First Order Phase Transition, to appear in Commun. Math. Phys.
Friedli S., Pfister C.-E., Non-Analyticity and the van der Waals
limit, to appear in J. Stat. Phys.
Isakov S.N., Nonanalytic Features of the First Order Phase Transition in
the Ising Model}, Commun. Math. Phys. 95, 427-443, (1984).
Isakov S.N., Phase Diagrams and Singularity at the Point of a
Phase Transition of the First Kind in Lattice Gas Models,
Teoreticheskaya i Matematicheskaya
Fizika, 71, 426-440, (1987).