Two Dimensions
- In the ferromagnetic case there is a phase transition: at low temperature, Peierls argument proves positive magnetization for the nearest neighbor case and then, by Griffiths inequality, also when longer range interactions are added; while, at high temperature, cluster expansion gives analyticity of the thermodynamic functions.
- In the nearest-neighbor case, the free energy has been exactly computed by Onsager, through the equivalence of the model with free fermions on lattice. The spin-spin correlation functions has been computed by McCoy and Wu.
Read more about this topic: Ising Model
Famous quotes containing the word dimensions:
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)
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