Statistical Physics F7035T

Luleå tekniska universitet
Avd. för Materialvetenskap
Hans Weber

Literature: Charles Kittel and Herbert Kroemer, Thermal Physics, Freeman 1980, and material from the homepage.
Teacher and examiner: Hans Weber, phone. 0920-492088, room E 163
Examination: Written exam (5.0hp) and one large project on Monte Carlo methods to be presented as a poster (2.5hp).
Prerequisite: Quantum Physics (F0047T) or Quantum Mechanics including writing simple computer programs in c or matlab (skills given in D0009E or D0017E).
Goals for students:
After the the course the student is expected to have reached
Knowledge of basic assumptions of statistical physics.
Have an understanding of the micro canonical, canonical and grand canonical ensemble.
The Bose-Einstein and Fermi-Dirac distribution functions and the classical limit.
Use concepts as the Helmholtz free energy, Gibbs free energy and entropy.
Do and understand a mean field calculation.
Make a simple Monte Carlo program applied to a model system and make
a scaling analysis. To be presented at a Poster session.
Related literature:

Random Generators:
One has to take great when using random number generators. Most computer languages
usually have 'built in' generators. These are however never used in serious Monte Carlo
simulations as they are poorly documented and poor quality. There are many well documented
generators around and below an example is given in a version in fortran and one in c.
For information on random generators see: wikipedia.

This text is available at: http://staff.www.ltu.se/~weber/kurs/statmek/kursprog.html

Lecture.		Contents	Problems
1		States of a model system	-
2		Entropy and Temperature, Boltzmann factor 29 - 42, 42 - 51, 58 - 68	2: 1, 2, 3
3	self	Helmholtz free energy, Ideal Gas 68 - 80	3: 1, 2, 3, 4, 8, 11
4		Monte Carlo simulations, and computer simulations in Statistical mechanics + handout	-
5		Thermal Radiation and Planck Distribution, Chapter 4 (not electrical noise)	4: 1, 2, 4, 5, 11
6		Chemical Potential and Gibbs distribution, Chapter 5	5: 3, 5, 6, 7, 8, 9, 11, 12, 13, 14
7	self	Ideal Gas, Chapter 6	6: 1, 2, 3, 6, 10, 12, 15
8	self	Gibbs Free energy and Chemical reactions, Chapter 9	9: 1, 2, 3
9 - 11		Phase Transformations, Chapter 10 + handout	10: 1, 3, 6, 7, 8
12 - 13		Fermi and Bose gases, Chapter 7	7: 1, 2, 3, 7, 8, 9
14		Binary Mixtures, Chapter 11	11: 2
15	self	Kinetic Theory, Chapter 14 pages 391-404 and 407	14: 1, 2, 3, 4
16		Poster session in physics corridor and course evaluation.	-

Handouts
This handout gives a good introduction to Monte Carlo simulations and also to analysing results:
Helmut G. Katzgraber : Introduction to Monte Carlo Methods

More background material (on Monte Carlo and finite size scaling) from ETH Zürich and
a book produced by students proseminar.pdf

Some useful links:
Arxiv , preprint server
APS Journals Journals at the American physical society (articles can only be retrieved from the university)
APS The American physical society

XY-Model 2D with n-n and next-n interaction ,
Ising Model 2D

Some people in the field

Peter Youngs Homepage

Helmut Katzgraber Homepage

James P. Sethnas Homepage

Stephen Teitels Homepage

Mats Wallins Homepage

Last edited 2020-01-20 by Hans Weber