Monte Carlo simulation methods

*W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C/Fortran; The Art of Scientific Computing, Cambridge University Press, New York, second edition, 1995*

An excellent swiss-army-knife of a book for numerical analysis.

Online version of Numerical Recipes-
*Gould, Tobochnik: An Introduction to Computer Simulation Methods: Applications to Physical Systems, Harvey Gould, et al.*

relatively simple introduction to computer simulation methods, including Monte Carlo. Uses a dialect of BASIC(!) -
*K. Binder und D.W. Heermann, Monte Carlo Simulation in Statistical Physics, Springer Series in Solid-State Sciences 80, Springer 1988.*A bit more advanced and mathematical textbook. *M. Creutz: Quarks, Gluons and Lattices, Cambridge Univ. Press 1983.*Introduction to field theory on the lattice, not much about simulation methods.- Other very useful lecture notes available on
the web:

Laskennallinen fysiikka (761668S), Fysiikan syventävä opintojakso Oulun yliopistossa. Sisältää paljon samoja aiheita kuin nämä luennot. (In Finnish)

Excellent lecture notes by Kai Nordlund, University of Helsinki. Check it! - Another set of lecture notes: Monte Carlo Simulation for Statistical Physics by Paul Coddington, Syracuse University.

**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.

Homework 1, to be returned by 27.9. Example results and code(C++) can be found from here.

Homework 2, to be returned by 18.10. Example results and code(C++) can be found from here. (Updated 1.11)

Homework 3, to be returned by 1.11. Example results and code(C++) can be found from here. (Updated 29.11)

Homework 4, to be returned by 29.11.

*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: