| Instructor: |
Olexei Motrunich
Office: Sloan Annex 127 Phone: (626) 395-8894 Email: motrunch |
|---|---|
| Class Meets: | Tue, Th 9:00 - 10:30, Downs 107 |
| Office Hours: | Tue 5:00-6:00
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| Teaching Assistant: | Tiamhock Tay
Office: Sloan Annex 130 Email: tay Office hours: Wed 4:00-5:00 |
| 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 |
| Other texts: |
K. Huang, "Statistical Mechanics". R. K. Pathria, "Statistical Mechanics" L. D. Landau and E. M. Lifshitz, "Statistical Physics. Part 1". N. Goldenfeld, "Lectures on phase transitions and the renormalization group". 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 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
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)
LECTURES:
(Disclaimer: My "lecture notes" are "scratch notes" I am working 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.
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: | Liquid-gas transition in the Van der Waals model.
Required reading: Same as lecture 3. |
| Lecture 5: | 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 6: | Lattice models and their phase transitions.
Required reading: Kardar volume 2, Chapter 5 (or 6?) and solved problems in Chapter 1. Lecture notes: Lattice models, spin models, and magnetic ordering. |
| Lecture 7: | 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 8: | 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 9: | Monte Carlo simulations.
Required reading: Kardar Chapter 6, section about Monte Carlo Lecture notes: Monte Carlo method |
| Lecture 10: | Finish Monte Carlo simulations (Ising example).
General Landau-Ginzburg theory of second-order phase transitions.
Required reading: Kardar Chapters 1,2 Lecture notes: Mike Cross' lecture 6. |
| Lecture 11: | Structure of Landau-Ginzburg theory; symmetries.
First order transition due to cubic invariants
and due to interactions.
Begin macroscopic manifestations and connection
to microscopic aspects of 2nd-order phase transitions.
Required reading: Kardar Chapters 2,3 Lecture notes: Microscopic aspects of criticality Demonstration link: Binary Mixture Critical Opalescence (about 1 minute from the start). |
| Lecture 12: | Fluctuation/dissipation theorem; correlation functions.
Ornstein-Zernike form of correlations functions.
Required reading: Kardar Chapter 3; Mike Cross' lecture 7. Lecture notes: Ornstein-Zernike theory |
| Lecture 13: | Ornstein-Zernike correlation functions. Continuous symmetry breaking
and Goldstone modes. Ginzburg criterion.
Required reading: Kardar Chapter 3. |
| Lecture 14: | The scaling hypothesis.
Required reading: Kardar Chapter 4 or Mike Cross' lecture 8. Lecture notes: Scaling hypothesis |
| Lecture 15: | 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 16: | RG for 1d Ising model; general structure and scaling forms.
Required reading: Same as lecture 15; Kardar Chapter 4 |
TR>
Lecture 17: | Conceptual RG and some formal aspects.
Required reading: Kardar Chapter 4 |
TR>
Lecture 18: | Gaussian model: solution by direct calculation and
solution by RG. Relevance/irrelevance of phi^4 perturbation.
Required reading: Kardar Chapter 4 |
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Lecture 19: | Pertubative RG for the phi^4 theory.
Wilson-Fisher fixed point.
Required reading: Kardar Chapter 5 Lecture notes: Gaussian fixed point ; pertubative RG and Wilson-Fisher fixed point ; Suggested reading: An excellent self-contained discussion of the RG can be found in Secs. I and II of Renormalization-group approach to interacting fermions by R. Shankar. |