Physics 220: Advanced Statistical Mechanics

Email: balents@kitp.ucsb.edu

Phone: 893-6381

TBA, in KITP (Kohn Hall), Room 2315

This course is the second quarter of statistical mechanics. It focuses on collective behavior of many-particle systems, hydrodynamics, and phase transitions.

This course is going to be taught a little differently than usual. We will cover aspects of the subject through topical examples from recent research. Rather than proceed systematically through the subject, we will introduce a research example, and work through the necessary background in as efficient (but not thorough!) a way as possible to get us to the point of understanding the example. This may be challenging, but it will hopefully also be stimulating. Systematic accounts of the fundamentals of the subject are found in many books, so you should be able to fill in the gaps by reading.

- Full set of Leon's lecture notes: in pdf
- John Cardy, "Scaling and Renormalization in Statistical Physics"
- Mehran Kardar, "Statistical Mechanics of Fields"
- Nigel Goldenfeld, "Lectures On Phase Transitions And The Renormalization Group"
- Subir Sachdev, "Quantum Phase Transitions"
- Lecture 4 and Chapter 2 here may be useful for a primer on second quantization.
- Spin ice:
- Order by disorder:

Physics 219. Knowledge of basic statistical mechanics, and quantum mechanics at a graduate level.

You are expected to complete the reading * in advance * of
the specified lecture

Lecture | Topic | Reading | Homework assigned | Homework due |

1 - 4/3/12 | Overview. Coldea experiment. Ising model, phases. Symmetry breaking. | |||

2 - 4/5/12 | Classical Ising transition. MFT. Fluctuations: classical chain at T>0. | lecture 1 , Coldea article | ps1 (due April 12) | |

3 - 4/10/12 | Quantum Ising model. Quantum transition. Fermionization. | lecture 2 (you may also want to read about 2nd quantization) | ||

4 - 4/12/12 | Critical phenomena. Scaling. Continuum field theory. | lecture 3 | ps2 (due April 24) | ps1 solution |

5 - 4/17/12 | Renormalization group and scaling | lecture 4 | ||

6 - 4/19/12 | Monte Carlo | lecture 5 | ||

7 - 4/24/12 | Elementary excitations. Domain walls versus spin flips. Effect of other chains | Hyejin Ju's notes on Monte Carlo (caveat emptor) | ps3 (due May 3) | ps2 solution |

8 - 4/26/12 | Finish Coldea experiment. Begin frustrated magnets and ice. | lecture 7 | ||

9 - 5/1/12 | Spin and water ice | lecture 8 | ||

10 - 5/3/12 | Spin ice. Spin liquid and correlations. | lecture 9 | ps 3 due | |

11 - 5/8/12 | Pinch points and monopoles | lecture 10 | ||

12 - 5/10/12 | Finish spin ice. Begin order by disorder | lecture 11 | ps4 (due May 17) | |

13 - 5/15/12 | domino model and J1-J2 model | lecture 12 | ||

14 - 5/17/12 | ObD in
Er_{2}Ti_{2}O_{7} | lecture 13 , arXiv:1204.1320 , arXiv:1204.0595 | ||

15 - 5/22/12 | Quantum critical points in metals - introduction | Lucile's notes on Er2Ti2O7 | ||

16 - 5/24/12 | Hertz theory. Upper critical dimension. | lecture 15 | ||

17 - 5/29/12 | Above the upper critical dimension | lecture 16 | ||

18 - 5/31/12 | Hertz theory for antiferromagnet in d=3 | lecture 17 | ps5 (due June 14) | |

19 - 6/12/12 | It still Hertz | lecture 18 | ||

20 - 6/14/12 | Beyond the Landau paradigm | lecture 19 | ||

lecture 20 |

Grades to be based on homeworks and class participation

Design by Nicolas Fafchamps