Syllabus

PEOPLE AND PLACES:

TEXTS: We will take material from two sets of online notes:

Daniel Ueltschi, Introduction to Statistical Mechanics, University of Warwick (2007)

Sacha Friedli and Yvan Velenik, Equilibrium Statistical Mechanics of Classical Lattice Systems: a Concrete Introduction, University of Geneva (2015)

Notes for additional topics may be posted online and additional material will be taken from the following sources:

D. Ruelle, Statistical Mechanics: Rigorous Results

B. Simon, Statistical Mechanics of Lattice Gases

TOPICS: Statistical Mechanics was developed in the early twentieth century to provide a theoretical basis for thermodynamics. Starting in the mid-twentieth century, it became a very active field in mathematics. Some of the major issues were the study of the nature of the thermodynamic limit and the existence and characterization of phase transitions. Although much is known, the problem of characterizing phase transitions remains an active area of research today. In this course, we will develop the thermodynamic formalism, mostly in the context of "lattice gas" models although some continuum mechanical models will also be discussed. Topics to be discussed include the Ising model, percolation, rotor models, the dependence of phase transitions on dimension and mean field bounds.

PREREQUISITES: In practice much of what we will do can be understood using only undergraduate analysis and linear algebra. However, measure theory does come in at some decisive points.

COURSE WEBSITE: https://sites.google.com/a/msu.edu/jeffrey-schenker/teaching/992-ss16

HOMEWORK: There will be problems and exercises posted on the website. These are optional, but it is highly recommend that you work on them. I will be happy to discuss the solutions in or out of class as appropriate.

PRESENTATIONS: Each registered student should give a 30 to 35 minute talk at some point in the semester. Potential topics will be mentioned as we go along, but you are encouraged to suggest a topic related to your own research if that is possible.