Advanced Statistical Physics
Statistical mechanics explains the simple behavior of complex systems. (J.P. Sethna)
In the family of physical theories Statistical Physics is something like the
eccentric cousin.
It deals not only with atoms, molecules or crystals but
also with more mundane things
like sand, cars and money.
(Rainer Scharf)
The principles of nonequilibrium statistical mechanics remain in the largest
measure unformulated. (Roy J. Glauber)
Clouds are not spheres, mountains are not cones, coastlines are not circles,
and bark is not smooth, nor does lightning travel in a straight line.
(Benoit B. Mandelbrot)
Time and place of lectures: Note change of date and venue!
Wednesdays 10.00-11.45 and Thursdays 8.15-9.45 in the seminar room of the II. Phys. Inst.
No lectures on November 5, 7, 28 and 29!
Problem class (by Su-Chan Park): Note change of date and venue!
Fridays 12.15-13.45 in the conference room of the Theory Institute
Problem class takes place on November 30, but not on December 7!
Recommended literature:
J.P. Sethna: Entropy, Order Parameters, and Complexity (Oxford University Press 2006)
N. Goldenfeld: Lectures on Phase Transitions and the Renormalization Group (Westview Press 1992)
M. Plischke and B. Bergersen: Equilibrium Statistical Physics
(3rd edition, World Scientific 2006)
D. Sornette: Critical Phenomena in Natural Sciences (2nd edition, Springer 2004)
Course announcement
Course summary
Introductory lecture on scale invariance (in German)
Problem sheets
Problems 1-4
Problems 5-6
Problems 7-9
Problems 10-12
Problems 13-15
Problems 16-18
Problems 19-20
Problems 21-23
Problems 24-26
Problems 27-29
Solutions 1-6
Solutions 7-9
Solutions 10-12
Solutions 13-15
Solutions 16-18
Solutions 19-20
Solutions 21-23
Solutions 24-29
Links and articles
Statistical Mechanics: Entropy, Order Parameters, and Complexity (website)
Self-avoiding walks (Java applet, Boston University)
Information Theory in Physics W.T. Grandy, Am. J. Phys. 65, 466 (1997)
Information Theory and Statistical Mechanics E.T. Jaynes, Phys. Rev. 106, 620 (1957)
Living polymers A. Ott, J.P. Bouchaud, D. Langevin, W. Urbach: Phys. Rev. Lett. 65, 2201 (1990)
Phase diagram of water (website)
Statistical mechanics of cellular automata S. Wolfram: Rev. Mod. Phys. 55, 601 (1983)
Toom's CA (IBM J. Res. Dev. 48, 2004)
Theory of phase-ordering kinetics A.J. Bray:
Adv. Phys. 43, 357 (1994)
Power laws, Pareto distributions and Zipf's law M.E.J. Newman:
Contemporary Physics 46, 323 (2005)
S. Wolfram: A new kind of science (website)
Movies of capillary waves (Science magazine)
Review article on diffusion-limited aggregation (T.C. Halsey, Physics Today, November 2000))
Power laws and wars (N.F. Johnson, APS News, November 2006))