Simulation Methods in Statistical Physics, spring 2014
Book: Frenkel and Smit: Understanding Molecular Simulations, available electronically from the library website) is well-written, and useful to read for this course. However, it does not cover everything that I am planning to discuss. In particular, there is no mention of Quantum MC.
Last year's course. Note: last year we used a different book!
I am providing scans of my lecture notes.
They are no substitute for reading the course literature or for attending the lectures.
The purpose of my lecture notes is to remind me of what to say to you. So you can probably use them to remember what I said.
If you have any comments or find any mistakes, please let me know.
Material (to be) discussed in the lectures and homework exercises
- Lecture 1, introduction
- what and why?
- Molecular Dynamics (MD) and Monte Carlo (MC)
- structure of a simulation
- practical programming issues
- example: Lorentz gas
- F&S: chapter 1, section 4.1, 4.2.1
- Lecture 2
- more examples from the Lorentz gas
- resource scaling example: hard spheres
- soft interactions: Lennard-Jones
- integration algorithms for MD: Verlet
- F&S: sections 4.2.2, 4.2.3
- Exercise due 29 Jan
- Lecture 3
- more on integration algorithms for MD: Verlet, Runge-Kutta
- symplectic integration
- F&S: sections 4.2, 4.3, A.3.2
- "Lecture" 4: lab
- Lecture 5
- Lyapunov instability
- cutoffs and long-range interactions, Ewald summation
- internal degrees of freedom of molecules, bonds
- F&S: sections 4.3, 12.1
- Lecture 6
- constraints: SHAKE
- F&S: section 15.1, 15.2
- Exercise due 12 Feb
- Lecture 7
- Finally! Statistical Physics!
- ensembles: microcanonical, canonical, grand canonical, Gibbs
- (block) averaging
- F&S: section A.3.3 D.3
- Lecture 8
- thermostats: Langevin, Nosé-Hoover
- F&S: section 6.1, 6.2
- Exercise due 19 Feb: Answer questions 8 and 9 on pages 58 and 59 of F&S. I haven't discussed tail corrections in the lectures, but they are explained in the book.
- Lecture 9
- Intro Monte-Carlo
- Monte Carlo integration
- Importance sampling
- Ising model as example
- F&S: 3.1
- Lecture 10
- Markov Chains
- (detailed) balance
- early rejection
- F&S 3.1, 3.2, 3.3, 5.1, 5.2
- Lecture 11
- cluster moves
- More ensembles
- F&S 5.3, 5.4, 14.3
- Exercise due 26 Feb
- "Lecture" 12: lab
- Lecture 13
- Free energy calculations
- intro Quantum Monte Carlo
- variational QMC
- F&S 7.1, 7.2, (7.3, 7.4), Thijssen 12.1, 12.2
- Exercise due 5 March
- Exercise due 19 March
- Lecture 14
- diffusion QMC
- path integral QMC
- Thijssen 12.3, 12.4.1
- deadline for programming projects
- Lecture 15
- question hour
- stroopwafels or some other cookies
- the exam
- extended mercy-deadline for the programming projects
Programming projects. The classical MC and MD projects are related. Read both descriptions all the way through before you start writing your code. Think about the structure of your programs before you start writing them. The project reports are due on the 24th of February and the 17th of March respectively. Include your code electronically. You can send everything in by email. Here is a list of things you might want to think about if you have bugs or get stuck.
There are exercises for bonus points. They are meant to give you an opportunity to practice the basic concepts from this course. Ask me questions about them any time. Hand them in one week after they have been posted.
If you do these well enough, you get a bonus on the exam.
The bonus is proportional to the amount of exercises you have done well, so it always pays to do them, even if you have not done the others. It will be a maximum of 15% of the total score. I will not hand out solutions, but you can continue to ask me questions about the exercises after the deadline, by email or in person.
Note that the exam questions will be similar in style. Here is the set from last year.
As mentioned in the first lecture, the weight of the exam and programming projects in the final grade is 50-50. You have to clear both to pass the course.