The course covers the basics of Monte Carlo simulations, with
concrete applications to simple spin models (Ising model, XY model)
and other selected models. The emphasis is on practical issues:
update algorithms, measurements, error analysis.
We will also consider some modern Monte Carlo methods,
like reweighting, multicanonical methods, and cluster algorithms.
The topics are applicable to almost any area of physics.
Requirements: Basics of numerical methods and statistical physics. Knowledge of some programming language (Fortran, C, C++, Java ...) is needed for the exercises.
Exercises: The exercises consist of mathematical/theoretical problems and programming tasks.
Problems? Come to talk to K.R. at TE317 at any time. A.L. can be reached at "Tuutortupa" as follows: Mon 12 - 13, Thu 13 - 14, Fri 10 - 11.
Part 1: Monte Carlo integration and random numbers (note added) (2.10: Corrected small error in Schrage's formula, p. 27. Thanks to D. Fernandez)
Part 2: Monte Carlo simulation (note added to older version in 23.10: addition to sect. 4.15, Autocorrelations. Included in the present version of part 2)
Part 3: Monte Carlo of particle systems
Part 4: Reweighting
Part 5: Jackknife and bootstrap; finite size scaling
Part 6: Multicanonical methods and cluster algorithms (NOTE: modifications also in the multicanonical part 26.11.)
Some example programs are available here
Fun with the Ising model: X-windows Ising model demonstration program (requires mersenne.h and mersenne_inline.c from the link above).
Textbooks and other course
There is no single textbook which covers the course material. Lecture notes will be the primary material. Additional material: