This is a demonstration of a nearest-neighbor interacting particle system simulating the Ising model for
magnetization. Lower temperatures (that is, larger values of the inverse temperature) correspond to stronger
nearest-neighbor interactions.
For low temperatures, the system exhibits spontaneous magnetization, that is, the
spins tend to align with one another. In this example, the boundary spins are fixed to positive, so spontaneous
magnetization leads eventually to all positive spins.
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.
Inverse temperature:
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.
