Prof. Ofer Biham

Office: Danciger B, room 210

Phone: 02-6584363

Email: biham@phys.huji.ac.il

Class times:

Monday 12:00 - 13:45

Thursday 8:00 - 8:45

Office hours: Monday 14:00-16:00, or any other time by a phone or email appointment.

Syllabus

Review of phase transitions and critical phenomena,

Ising models, Markov processes.

Monte Carlo methods for equilibrium statistical physics:

Metropolis, heat-bath algorithms.

Cluster algorithms: Swendsen-Wang, Wolff algorithms.

Simulations of statistical physics out of thermal equilibrium:

kinetic Monte Carlo methods and applications to diffusion and

pattern formation problems with conserved order parameter.

Rate equation and master equation methods for particle diffusion,

cluster nucleation and chemical reactions. Simulations of stochastic

systems using Langevin and Fokker-Planck equations.

Simulations of thin film growth using kinetic Monte Carlo methods.

Chemical reaction networks on surfaces. The role of fluctuations

in reaction networks on small grains and the master equation.

Growth of rough surfaces, scaling and the Kardar-Parisi-Zhang

equation.

Spin glasses, minimization problems: Simulated annealing and

other techniques.

Simulations of dynamical systems using cellular automata:

applications to traffic flow, sandpiles and granular flow.

Random number generators, tests of randomness, generating

desired distributions: Gaussian distribution, power-law

distributions.

Fractal growth phenomena, fractal analysis, emergence of

power-law distributions in dynamical models, distribution

of wealth, stock market fluctuations, Levy flights, the Pareto

distribution and the Zipf plot.

Bibliography

- M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics

- H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena

- J.J. Binney, N.J. Dowrick, A.J. Fisher and M.E.J. Newman, The theory of critical phenomena

- W.H. Press, B.P. Flannery, S.A. Teukolsky
and W.T. Vetterling, Numerical Recipes: the art of
scientific computing

- F.S. Acton, Numerical methods that work

- N. Gershenfeld, The nature of mathematical modeling

- M. Mezard, G. Parisi and M.A.
Virasoro, Spin Glass theory and beyond

Credit and Grades

There will be four homework problem sets. The final grade will consist

of the grade of the final exam (60 percent) and the grades of the

homework sets (10 percent each).

Homework

Problem set no. 1

Problem set no. 2

Problem set no. 3

Problem set no. 4

URL: http://www.phys.huji.ac.il/~biham/CPhome.html