Classical Statistical Models

Dr. Wolfgang Unger

unger at physik.uni-bielefeld.de

Room E6-118

Lecture:	Wed. 10:15-11:45 in Room T2-208
Exercises:	Mo. 15:00-16:00 in Room C01-148 (with Dr. Jangho Kim)

Content:	► Statistical Processes and Random Walks ► Percolation ► Spin Models, Dimer Models, Vertex Models ► Phase Transitions, Universality ► Low- and High Temperature Expansion, Dual Formulations, Transfer Matrix Method
Prequisites:	Course in Statistical Mechanics

					3-state Potts Model on 20x20 square lattice, Metropolis algorithm
T=0.8	T=1.0	T=1.2	T=1.4	T=1.6
					3-state Potts Model on 20x20 square lattice, Worm algorithm

► Lecture 1 (12. April '16): Introduction, Probability Distributions

► Lecture 2 (20. April '16): Stochastic Processes

► Lecture 3 (27. April '16): Markov Chains

► Lecture 4 (04. May' 16): Random Walks

► Lecture 5 (11. May '16): Critical Phenomena

► Lecture 6 (18. May '16): Ising Model, Lattice Gas

► Lecture 7 (25. May '16): Ising Model: Transfer Matrix, Mean Field

► Lecture 8 (01. June '16): Ising Model: Low- and High-T expansion, Duality

► Lecture 9 (08. June '16): Dimer Models

► Lecture 10 (15. June '16): Potts Model

► Lecture 11 (22. June '16): Percolation

► Lecture 12 (29. June '16): Vertex Models

► Lecture 13 (06. July '16): Hard Discs

► Lecture 14 (13. July '16): Hard Spheres

► Lecture 15 (20. July '16): Outlook: Quantum Models, Self-ogranized Criticality

► To qualify for the oral exam (you can earn 5 CP),
you should attend the exercises regularly.

► The sheets consist of about 50% computing exercises and 50% paper and pencil exercises.
The points of each sheet sum up to 20 points.

► Jangho Kim will provide solutions to selected exercises which involve small computer simulations

Andrey Andreyevich Markov ► Sheet 1 (Markov Chain) Solutions to Computing Exercises	Stanislaw Marcin Ulam ► Sheet 2 (Monte Carlo Method) Solutions to Computing Exercises	Ludwig Eduardo Boltzmann ► Sheet 3 (Boltzmann Distribution)

Ernst Ising ► Sheet 4 (Ising Model)	Renfrey Potts ► Sheet 5 (Potts Model)	Pieter Willem Kasteleyn ► Sheet 6 (Fortuin-Kasteleyn Representation)