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:
“Words are finite organs of the infinite mind. They cannot cover the dimensions of what is in truth. They break, chop, and impoverish it.”
—Ralph Waldo Emerson (1803–1882)
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)