1. Computational Physics - Monte Carlo Methods Dr. Guy Tel-Zur Lecture 9 Murmur by Piotr Wojtkowski, http://www.publicdomainpictures.net. Version 08-12-2010-16:45

2. References MHJ Chapter 10 R. Landau et. al “A Survey of Computational Physics”, Chapters 5 and 13 S. Koonin, Chapter 8 Giordany & Nakanishi, Chapters 7 & 8

3. Random Walk Self Avoidance Walk (SAW), non-intersecting

4. Ising model and phase transitions in magnetic systems

7. The Magnetization:

8. 2D square lattice with Periodic Boundary Conditions (PBC) The Partition function for N spins in 1D with free ends (see textbook): The Partition function for N spins in 1D with PBC:

10. A phase transition is marked by abrupt macroscopic changes as external parameters are changed, such as an increase of temperature. The point where a phase transition takes place is called a critical point.

11. The Ising model and phase transitions

14. The Metropolis algorithm and the two-dimensional Ising Model

17. MHJ “ising_2dim.cpp” can not be compiles. “matrix” is undefined and free_matrix as well….  Analyze the Parallel 2D Ising model program I am looking for a student that will work on Parallel Ising model for his final project!

18. Time-correlation functions