New Approaches to Modern Physics/ISING MODEL


118093 - New Approaches to Modern Physics
WINTER 2005

Advanced Statistical Mechanics


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[JOAN ADLER's lectures]

Ising Model

  1. Definitions
  2. The Ising model has exact solutions in 1D and 2D. These do not give the same results as mean-field theory for the critical exponents and this observation opened the way for the modern study of phase transitions.
  3. In 3D there are only numerical approaches such as simulations and series expansions. I will not discuss the algorithms of these here (thats for the Computational Physics course) but I will show some important features. Both give the same numbers up to many figures of precision so I guess we are getting it right.
  4. Easy interactive simulations in 2D
    1. zero field - Mike Creutz .
    2. finite field - Sasha Gemintern adapted this program for a finite field and canonical ensemble.
    3. These both run on any linux machine or on tx, see also a local download link for the Creutz routines. The compile command is: cc -O -o xising -L/usr/X11R6/lib xising.c -lm -lX11
  5. Beautiful simulations in 3D - Lior Metzger did an undergraduate project of visualizations of Ising models. This is also not difficult to run, but for now I will just show some pictures.
  6. Newest 3d Ising - project of Ido Rozen