Measure Theoretic Description
The one dimensional Potts model may be expressed in terms of a subshift of finite type, and thus gains access to all of the mathematical techniques associated with this formalism. In particular, it can be solved exactly using the techniques of transfer operators. (However, Ernst Ising used combinatorial methods to solve the Ising model, which is the "ancestor" of the Potts model, in his 1925 PhD thesis). This section develops the mathematical formalism, based on measure theory, behind this solution.
While the example below is developed for the one-dimensional case, many of the arguments, and almost all of the notation, generalizes easily to any number of dimensions. Some of the formalism is also broad enough to handle related models, such as the XY model, the Heisenberg model and the N-vector model.
Read more about this topic: Potts Model
Famous quotes containing the words measure and/or description:
“The measure of a master is his success in bringing all men round to his opinion twenty years later.”
—Ralph Waldo Emerson (1803–1882)
“The type of fig leaf which each culture employs to cover its social taboos offers a twofold description of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”
—Freda Adler (b. 1934)