The spins (except for the fixed boundary) are intitially set randomly to plus or minus. With an initial inverse temperature of 0.2, spontaneous magnetization does not occur. If the inverse temperature is changed, for example, to 1.0 and the system reset, spontaneous magnetization will be observed.

This demonstration works best in Google Chrome as there are some formatting issues with Mozilla Firefox.

Notes:

- See Snell and Kindermann,
*Markov Random Fields and Their Applications*, American Mathematical Society, 1980, for details on the algorithm used in this demonstration. - The demonstration uses the random number generator which is part of the Dart mathematics library. I do not know the limitations of that generator, but, most likely, it should be suspect for an application such as this which requires long sequences of random numbers.

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