Ideas and results of the mathematical theory of phase transitions
Manfred Salmhofer, Heidelberg University
Abstract:
Although only a handful of models of statistical mechanics are solvable in the sense that one can calculate their correlation functions explicitly, important information about phase diagrams and phase transitions has been obtained exactly, by rigorous, yet relatively simple mathematical methods. In this course, I will give an overview of classics in this field, such as the Peierls argument, the Yang-Lee and Mermin-Wagner theorems, and the infrared bound, and also explain some recent developments.