Monte Carlo Methods
in Statistical Physics and Field Theory

Lecturer:

Dr. Wolfgang Unger

unger at th.physik.uni-frankfurt.de

Room 02.105

Lecture:	Wed. 9:15-10:45 in Room 02.114
Exercises:	Mo. 14:00-15:00 in Room 02.114

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 (16. Oct. '13): Introduction, Historical Remarks, 5 Ways to compute π

► Lecture 2 (23. Oct. '13): Basic Sampling, Monte Carlo Integration

► Lecture 3 (30. Oct. '13): Importance Sampling, Basic Facts in Probability Theory

► Lecture 4 (06. Nov. '13): Markov Chains, Markov Chain Monte Carlo

► Lecture 5 (13. Nov. '13): Percolation, Random Walks, Equilibrium Monte Carlo

► Lecture 6 (20. Nov. '13): Hard Discs and Spheres, Heatbath Algorithm

► Lecture 7 (27. Nov. '13): Ising Model (Low/High Temperature Expansion, MC in d>2)

► Lecture 8 (04. Dec. '13): Potts Model

► Lecture 9 (11. Dec. '13): Cluster Algorithm, Worm Algorithm

► Lecture 10 (18. Dec. '13): Entropic Forces, Dimer Systems

► Lecture 11 (15. Jan. '14): Path Integrals, Anharmonic Oscillator

► Lecture 12 (22. Jan. '14): Relativistic Bose Gas

► Lecture 13 (29. Jan. '14): Lattice Gauge Models

► Lecture 14 (05. Feb. '14): Compact QED

► Lecture 15 (12. Feb. '14): Yang-Mills Theory, SU(2), Outlook for QCD

Exercises:

► To qualify for the oral exam (you can earn 4 CP, subject to the decision of the Prüfungsamt),
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)	Renfrey Potts Sheet 9 (Potts Model)

Richard Philips Feynman Sheet 10 (Feynman Path Integral)	Satyendra Nath Bose Sheet 11 (Bosons)	Sheet 12 (Hopping Parameter Expansion)