5 Nucleation

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"ising" can also be initialized in the fully magnetized configuration. What happens if we apply a field opposed to this magnetization? The full system can lower its energy by reversing the magnetization, but for any individual spin the loss of exchange energy associated with a spin flip outweighs the advantage of being parallel to the external field.

run and you see the thermal fluctuations that occasionally reverse a spin here or there, but the spin quickly flips back again. You also see clusters develop and evaporate again. With patience, a cluster will grow large enough, a "critical size" cluster, that the energy cost in exchange associated with growing larger is LESS than the gain in interaction energy with the external field. The critical cluster then takes over the whole field. If you want to stop the run, hit stop.