Fysiikan simulaatiomenetelmät
Simulation methods in physics

Description: This course is (mostly) an introduction to Monte Carlo simulation methods, especially simulations on (regular) lattices. Lattice Monte Carlo simulations are an important tool in many areas of physics, including condensed matter physics, high-energy physics, biophysics etc. The course covers the basics of Monte Carlo simulations, with concrete applications to simple spin models (Ising model, XY model), update algorithms, 'modern' Monte Carlo methods (cluster algorithms, multicanonical methods), measurements, reweighting and error analysis. This part is quite generic, applicable almost to any area of physics.

Additionally, depending on the wishes of the students, we may discuss physics on the lattice in general; i.e. how a continuum theory is discretised and analysed using lattice methods. Theories discussed here may include Ginzburg-Landau theory (effective theory of superconductivity) and QCD.

Language: English or Finnish, depending on the students
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.

Lecture notes NEW: available both in .pdf and 2-on-1-page .ps
Introduction .ps.gz .pdf
Monte Carlo integration and random numbers .ps.gz .pdf (last updated 11.2., 64 pages, 3 new)
Fundamentals of the Monte Carlo simulation .ps.gz .pdf (last updated 19.2., 58 pages)
Cluster algorithms .ps.gz .pdf (last updated 25.2.,25 pages)
Reweighting, Jackknife, Bootstrap .ps.gz .pdf (last updated 3.3.,31 pages)
Low and high-T expansions .ps.gz .pdf (last updated 19.3.,21 pages)
Quantum field theory on the lattice .ps.gz .pdf (last updated 7.4.,55 pages)
Finite temperature phase transition .ps.gz .pdf (9 pages)
Finite size scaling .ps.gz .pdf (last updated 5.5, 40 pages)
Multicanonical methods .ps.gz .pdf (20 pages)

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).
If you are logged on the alpha-cluster, you can also execute it directly with command "~/rummukai/xisingdemo".

Preliminary contents:
Introduction to Monte Carlo methods
Random numbers, random ensembles, Monte Carlo integration
Importance sampling, detailed balance, autocorrelations
Measurements, error analysis and autocorrelations
Ising model, simple update algorithms
Laying out the fields on a computer
Cluster update algorithms - beating the autocorrelations
Reweighting, multihistogram reweighting
Potts models, first order phase transitions
Multicanonical methods
Parallel ensembles
Parallel programming - Open MP, MPI
Real time evolution on the lattice: Molecular Dynamics etc.
...
Field theory on a lattice - to be filled in

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

• 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.
• Additional information about Monte Carlo methods is available on the web, in the form of the excellent lecture notes by Kai Nordlund. Check it!
• Another set of lecture notes: Monte Carlo Simulation for Statistical Physics by Paul Coddington, Syracuse University.