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Coarsening in the Ising Model

Demagnetize the sample by running briefly at H = 0 and T = 10 (or hit T=inf). Now set T below T_c (say, T=0) and let it run. Describe how the pattern changes with time. (As the pattern develops, the changes occur more slowly and you may want to increase "Sweep Increment" using the configure button to 10 or more.) By

  1. measuring on the screen by eye,
  2. by writing a subroutine to measure correlation functions and finding the half-maximum, or
  3. using the energy as a measure of the total length of the surface between spin up and spin down regions (valid only at low temperature),
find the typical size L(t) of the red and white domains, and graph it versus time. What power law do we expect it to grow with? Does it grow as expected? When do finite-size effects start changing things? Takahiko Koyama has a clear analysis of this coarsening process, including a simple analysis of the decay of a circular island.

Other Ising Model Presets

Description of the Model.
Phase Diagram
Magnetization M(T)
Nucleation
Domain Coarsening
Questions for Further Research

Links

The Ising Model
New Tools in Physics: Course Description
Cornell Undergraduate Physics Teaching Lab.
LASSP Home Page, and Entertaining Science Done There,
Last modified: September 11, 1995

James P. Sethna, sethna@lassp.cornell.edu.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).