Monte Carlo Methods
in Statistical Physics and Field Theory

Lecturer:

Dr. Wolfgang Unger

unger at physik.uni-bielefeld.de

Room E6-118

Lecture:	Wed. 10:15-11:45 in Room D6-135
Exercises:	(Giuseppe Gagliardi) Mo. 14:15-15:15 in Room D6-135

Content:	► Markov Chains, Sampling ► Algorithms (Metropolis, Heatbath, Cluster, Worm) ► Models (Hard Spheres, Spin Systems, Dimer Systems, Bose Gas, Lattice Gauge Models) ► Phase Transitions, Critical Phenomena
Prequisites:	Course in Quantum Mechanics and Statistical Mechanics, Basic Programming Skills (any language will do)

					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

Lectures: (preliminary, subject to change)

The lecture notes will be published successively after each lecture.

► Lecture 1 (11. Oct. '17): Introduction, Historical Remarks, 5 Ways to compute π

► Lecture 2 (18. Oct. '17): Basic Sampling, Monte Carlo Integration

► Lecture 3 (25. Oct. '17): Importance Sampling, Basic Facts in Probability Theory

► Lecture 4 (01. Nov. '17): Markov Chains, Markov Chain Monte Carlo

► Lecture 5 (08. Nov. '17): Percolation, Random Walks, Equilibrium Monte Carlo

► Lecture 6 (15. Nov. '17): Hard Discs and Spheres, Heatbath Algorithm

► Lecture 7 (22. Nov. '17): Ising Model (Low/High Temperature Expansion, MC in d>2)

► Lecture 8 (29. Nov. '17): Potts Model

► Lecture 9 (06. Dec. '17): Cluster Algorithm

► Lecture 10 (13. Dec. '17): Worm Algorithm

► Lecture 11 (20. Dec. '17): Entropic Forces, Dimer Systems

► Lecture 12 (10. Jan. '18): Path Integrals, Anharmonic Oscillator

► Lecture 13 (17. Jan. '18): Relativistic Bose Gas

► Lecture 14 (24. Jan. '18): Lattice Gauge Models

► Lecture 15 (31. Jan. '18): Compact QED, Outlook to Yang-Mills Theory

Exercises:

► To qualify for the oral exam (you can earn 5 CP)
you need to get 50% of the points from the homework.

► The sheets consist of about 70% computing exercises and 30% paper and pencil exercises.
The points of each sheet sum up to 20 points.

► Computing exercises should be handed in as a short report, explaining the approach and summarizing the result.
Also, the code should be sent to me prior to the tutorial on mondays.
We will discuss the solutions immediately, hence I cannot accept solutions after this deadline.

Goerges-Louis Leclerc, Comte de Buffon ► Sheet 1 (Buffon's Needle Experiment)	Stanislaw Marcin Ulam ► Sheet 2 (Monte Carlo Method)	Nicholas Constantine Metropolis ► Sheet 3 (Metropolis Algorithm)

Andrey Andreyevich Markov Sheet 4 (Markov Chain)	W. Keith Hastings Sheet 5 (Metropolis-Hastings Algorithm)	Ludwig Eduardo Boltzmann Sheet 6 (Boltzmann's statistical mechanics)

James Clerk Maxwell Sheet 7 (Maxwell Distribution)	Ernst Ising Sheet 8 (Ising Model)