Description:
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.
Lecture notes
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
material:
There is no single textbook which covers the course material.
Lecture notes will be the primary material. Additional material: