| Instructor: |
Olexei Motrunich
Office: West Bridge 149-33 Phone: (626) 395-8894 Email: motrunch |
|---|---|
| Class Meets: | Mon, Th 14:30 - 16:00, Downs 107 |
| Office Hours: | Tue 4:30-5:30
|
| Teaching Assistants: | Scott Geraedts
Office: West Bridge 058
Email: scott geraedts gmail
Office hours: Wed 4:00-5:00 Shankar Iyer Office: West Bridge 156 Email: siyer shankar gmail Office hours: Wed 3:00-4:00 |
| Textbook: |
M. Kardar, "Statistical Physics of Particles".
New York, NY: Cambridge University Press, 2007. ISBN 9780521873420
M. Kardar, "Statistical Physics of Fields". New York, NY: Cambridge University Press, 2007. ISBN 9780521873413 N. Goldenfeld, "Lectures on phase transitions and the renormalization group". |
| Other texts: |
K. Huang, "Statistical Mechanics". R. K. Pathria, "Statistical Mechanics" L. D. Landau and E. M. Lifshitz, "Statistical Physics. Part 1". J. Cardy, "Scaling and Renormalization in Statistical Physics". S.-k. Ma, "Modern Theory of Critical Phenomena". |
| Homework and Grading: | There will be a weekly homework assignment anounced in class (and via email), due one week later. There will be a final exam. Grades will be based on the homework (70%) and final exam (30%). |
| Course Policies: | We will adhere to standard course policies such as Mike Cross' Ph106a course policies . Note in particular late homeworks and extensions policy: No grade if submitted later than one week after the due date; 50% grade for any late homeworks up to one week late; one "free" (full-credit) late homework up to one week late (indicate on the title page page that this is the "free" late homework). |
Course Description:
This term covers physics of interacting particles, phases, and phase transitions.
Topics include: interacting gases and liquid-gas transition; lattice models; Ginzburg-Landau description of phases and broken symmetries; classical field theories; and renormalization group approach to critical phenomena.
Prerequisites:
Phy 127a or equivalent
Working course plan:
Phy127b 2010 course plan
Links to Statstical Physics courses on the web
Mike Cross' Phy127b 2005 lectures
Mehran Kardar's MIT lectures (Statistical Mechanics of Particles)
Mehran Kardar's MIT lectures (Statistical Mechanics of Fields)
PROBLEM SETS:
LECTURES:
(Disclaimer: My "lecture notes" are "scratch notes" I worked through when preparing the lectures, so no originality or good organization is intended. They are posted only to give you some idea what we have covered and fill in some missing steps in the lectures, and also to point to material not in the main text.)
| Lecture 1: | Interacting classical gas: Perturbative treatment in interaction (cummulant expansion).
Required reading: Chapter 5 of Kardar vol.1. Cumulant expansion is discussed formally in Chapter 2, vol.1. Lecture notes: Overview and cummulant expansions |
|---|---|
| Lecture 2: | Mayer's cluster expansion. Virial expansion for the equation of state.
Required reading: Chapter 5 of Kardar vol.1. Suggested reading: Mike Cross' lectures 1 and 2 give a nice broad-brush review of the overall structure of the cluster expansion as well as discuss other methods used to describe the liquid state. Lecture notes: Mayer cluster expansion |
| Lecture 3: | Van der Waals equation of state. Liquid-gas transition in the
Van der Waals model.
Required reading: Chapter 5 of Kardar vol.1. Suggested reading: Mike Cross' lecture 3. Lecture notes: Van der Waals equation ; Thermodynamics of VdW gas ; Variational meanfield approach ; Review of applications of thermodynamics to 1st order transitions. |
| Lecture 4: | Variational mean field approach in Statistical Mechanics
and application to the Van der Waals gas. Critical point behavior.
Required reading: Same as lecture 3. Lecture notes: Critical point behavior. |
| Lecture 5: | Lattice models and their phase transitions (spin models and magnetic
ordering).
Required reading: Kardar volume 2, Chapter 6 and solved problems in Chapter 1. Lecture notes: Lattice models, spin models, and magnetic ordering. |
| Lecture 6: | Mean field description of the ordering transition
Required reading: Kardar volume 2, Chapters 1,2; Mike Cross' lecture 5,6 Lecture notes: Mean field for Ising model. |
| Lecture 7: | Ising model in 1d and 2d.
Required reading: same as Lecture 7 and Kardar Chapter 6, section about 1d systems and transfer matrices Lecture notes: Ising model in 1d and 2d. |
| Lecture 8: | Monte Carlo simulations.
Required reading: Kardar Chapter 6, section about Monte Carlo Lecture notes: Monte Carlo method |
| Lecture 9: | General Ginzburg-Landau theory of second-order phase transitions.
Coarse-graining and GL functional. GL equations and correlation length.
Structure of Landau-Ginzburg theory; symmetries.
Required reading: Kardar Chapters 1,2 Lecture notes: Mike Cross' lecture 6; Landau-Ginzburg Theory |
| Lecture 10: | First order transition due to cubic invariants and due to interactions.
Macroscopic manifestations and connection to microscopic aspects of
2nd-order phase transitions. Fluctuation/dissipation theorem;
correlation functions.
Required reading: Kardar Chapters 2,3 Lecture notes: Microscopic aspects of criticality Demonstration link: Binary Mixture Critical Opalescence (about 1.5 minute from the start). |
| Lecture 11: | Ornstein-Zernike theory of correlations functions.
Continunous symmetry breaking and Goldstone modes.
Required reading: Kardar Chapter 3; Mike Cross' lecture 7. Lecture notes: Ornstein-Zernike theory |
| Lecture 12: | Failure of the mean field. Ginzburg criterion.
Required reading: Kardar Chapter 3. |
| Lecture 13: | The scaling hypothesis.
Required reading: Kardar Chapter 4 or Mike Cross' lecture 8. Lecture notes: Scaling hypothesis |
| Lecture 14: | Renormalization group for 1d Ising model.
Required reading: Kardar Chapter 6 or Mike Cross' lectures 9,10. Lecture notes: RG for 1d Ising model. |
| Lecture 15: | Conceptual RG and some formal aspects.
Required reading: Kardar Chapter 4 Lecture notes: Conceptual RG. |
| Lecture 16: | Examples of real-space RG in 2d: Migdal-Kadanoff bond-moving RG
and Niemeijer-van Leeuwen cummulant approximation.
Required reading: Kardar Chapter 6.4, 6.5 Lecture notes: Real-space RG in 2d Ising. |
| Lecture 17: | Gaussian model: solution by direct calculation and scaling form.
Solution by RG. Relevance/irrelevance of phi^4 perturbation.
Required reading: Kardar Chapter 5 Lecture notes: Gaussian fixed point |