# Statistical Mechanics

The following are resources from PHYS - 326 (Statistical Mechanics), a course I assisted in teaching during the Winter of 2017. There are a number of notes/textbook suggestions among other things. Posts run in cronological order. The main course page, hosted by Professor Grant, can be found here.

## Tutorial #1 - Scientific Computing with Python

In the first tutorial we did a brief overview of Python programming and some of the relevant tools for scientific programming with Python links to relevant documentation and downloads can be found below.

- Anaconda Distribution of Python Download
- More about Jupyter Notebooks
- Atom text editor
- Numpy User Guide (How to get started)
- Scipy Tutorial and Documentation
- Beginners Guide to Matplotlib

If you a good reference to get started with all of these tools take a look at the “Getting started with Python for Science” notes from Scipy. They step through all the basics of Python with a focus on doing science.

## Extra Reading

There is a mountain of both good and bad explanation of statistical mechanics topics floating around in the world. I’ll list here the resources I’ve found the most useful for references outside of Prof. Grant’s notes and Schroeder.

### David Tong’s Lecture Notes

David Tong’s Lecture Notes are a great place to start if you’re looking for an explanation on any topic. Can be a little sort on examples but the explanation of concepts is very good.

### Kardar - Statistical Physics of Particles

Statistical Physics of Particles is a solid, modern textbook on statistical physics. You can also find the associated lectures by the author Mehran Kardar here. The textbook has many examples of calculations as well as practice problems to work on.

### Huang - Statistical Mechanics

Part B and C of Kerson Huang’s Statistical Mechanics cover equilibrium stat mech and phase transitions (and other special topics) respectively. Practice problems can be found at the end of each chapter.

## Tutorial #3

Notes on the 2-state system example can be found here

## Tutorial #6

Notes on Monte Carlo methods and solutions to the second problem set can be found here

## Finite size effect and the Ising Model

There was a lot of trouble with the finite size effect on assignment 4. Take a look here for a discussion about the finite size affect and a simple implemenation of the the Ising model in the Julia programming language.

## Extra Extra Reading

Here is a list of addition resources pertaining to the second half of the course. For almost all of them you’ll need to search for them through the McGill library to gain access, access them while on the campus network or through the VPN.

### Critical Dynamics - Uwe Tauber

Section 2.4 contains a discussion of Langevin equations and Brownian motion in particular. The rest of chapter 2 contains an in depth discussion of stochastic processes in general including markov processes, the master equation, the Fokker-Plank equation and detailed balance. Some of the details are a little advances, including a few references to functional integration. If you see swirly D’s, ignore them as best you can.

### Statistical Physics of Fields - Mehran Kardar

Statistical Physics of Fields is the follow up to Kardar’s Statistical Physics of Particles. This is a fairly advances text book as well, but covers field theories and the Kosterlitz-Thouless transition in particular for those that took interest in the topics right at the end of the course. You can also find discussion of mean-field theories here.

### Stochastic Processes in Physics and Chemistry - N.G. Van Kampen

Van Kampen’s text is a classic in stochastic processes. Good, indepth description of Brownian motion among other goodies. See chapter 9 titled “The Langevin Approach”.

### Theory of Simple Liquids - Hansen and McDonald

Chapter 4 contains a derivation of the scattering cross section using the wave function of neutrons. This is very much the same as what you should have seen in quantum mechanics. There are references to a “g®” which is the radial distribution function. You don’t need to know what this is but you can learn all about it in earlier chapters of this book. If you’re interested in perturbation theory in statistical mechanics, this is an excellent place to learn!

Everyone should read the first 3 pages of Chapter 2….just because its great.