Spring 2020

Class meets MWF 2:30-3:20PM and T 12:30-1:20 in Wean Hall 6327

Website http://euler.phys.cmu.edu/widom/teaching/33-342

Professor Michael Widom, Office 6305 Wean Hall

e-mail: widom@cmu.edu, Phone: 412-268-7645

Office Hours: Any time I'm not busy

**ONLINE MATERIALS:** Due to the coronavirus outbreak various class notes will be placed on this new page.

**What you will learn:**
This course presents advanced topics in Statistical Mechanics, with an initial focus on quantum statistics of fermions and bosons. Applications will be made to the quantum ideal gas and its Bose condensation, and to the physics of electrons and phonons in solids, and blackbody radiation. We then turn to the study of the Ising model and calculate its properties in the limits of low and high temperature. Finally, phase transitions of the Ising model and other interesting topics will be studied using Monte Carlo simulation. Analytical, numerical, and simulation-based approaches will be utilized.

**What you should know:**
Prior familiarity with quantum
mechanics is assumed at the level of 33-234 or 33-225, and statistical
mechanics/thermodynamics at the level of 33-341.

**Books:** The principal content of the course will be drawn from Swendsen, *An Introduction to Statistical Mechanics and Thermodynamics*. Other books of interest include Kardar, *Statistical Mechanics of Particles*, and Goodstein, *States of Matter*, books designed for similar courses at MIT and CalTech, respectively, and McQuarrie, *Statistical Mechanics*, a graduate level text. *Statistical Mechanics: Entropy, Order Parameters, and Complexity* by Sethna, based on a course at Cornell, is available for free download.

**Grading:** Letter grades will be based on homework (20%), two midterm exams (20% each) and a final exam (40%). Homework and reading (listed here) will be assigned almost daily and discussed in class.

**Course Outline:** (Actual day-by-day class coverage can be found here)

**Quantum Statistical Mechanics**- Spin 1/2 in magnetic field
- Harmonic oscillator
- Blackbody radiation
- Phonons in solids
- Quantum ideal gas
- Bose-Einstein transition
- Electrons in solids

**Models of phase transitions**- Ising/Potts/Roughening models
- Transfer matrix
- Mean Field Theory
- Low/High temperature expansions
- Monte Carlo simulation