| PHYS 652 - Advanced Statistical Mechanics |
|---|
| Semester: | Fall 2012 | ||
|---|---|---|---|
| Instructor: | Cemal Yalabik | ||
| Office: | Room SA-228 | ||
| Office Hours: | Wednesday | 10:40 - 11:30 | Room SA-228 |
| All other times | (if available - call 1316 to check) | Room EA-G11 | |
| Assignments: | Assignments | ||
| Course Schedule: | |||
| Tuesday | 10:40 -12:30 | Room SA-Z19 | |
| Wednesday | 9:40 - 10:30 | Room SA-Z02 | |
| Recommended Prerequisite: | |||
| Phys 552 or equivalent graduate course on Statistical Mechanics. | |||
Grading will be based on a number of projects assigned during the course. The projects will involve computer implementations of the methods discussed in class as well as independent study of a number of topics. (Topics will be suggested by the students.)
| Week | Subject | Random variables and their transformations The Langevin and Fokker-Planck equations The master equation, detailed balance Boltzmann transport equation, the H-function, and its solutions The Wigner function The Ising model - solution to the 1-D model (No Wednesday class) The 2-D Ising model - high and low temperature series (No Monday class) The 2-D Ising model - mean field theory Introduction to phase transitions and critical phenomena - the critical exponents The Monte-Carlo method, simulated annealing and molecular dynamics The renormalization group theory* and its application to the Ising model Other model systems with more complicated phase diagrams - multicriticality Dynamic criticality - self ordered criticality Project presentations Project presentations|
*K. G. Wilson, in Renormalization Group Methods, in Advances in Mathematics, 16, 170 (1975).
"It (RG) is at present an approach of last resort, to be used only when all other approaches have been tried and discarded. The reason for this is that it is rather difficult to formulate RG methods for new problems; in fact the RG approach generally seems as hopeless as any other approach until someone succeeds in solving the problem by RG approach."