Exactly solvable models

Potts model

In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics. The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is exactly solvable, and that it has a rich mathematical formulation that has been studied extensively. The model is named after Renfrey Potts, who described the model near the end of his 1951 Ph.D. thesis. The model was related to the "planar Potts" or "clock model", which was suggested to him by his advisor, Cyril Domb. The four-state Potts model is sometimes known as the Ashkin–Teller model, after Julius Ashkin and Edward Teller, who considered an equivalent model in 1943. The Potts model is related to, and generalized by, several other models, including the XY model, the Heisenberg model and the N-vector model. The infinite-range Potts model is known as the . When the spins are taken to interact in a non-Abelian manner, the model is related to the , which is used to discuss confinement in quantum chromodynamics. Generalizations of the Potts model have also been used to model grain growth in metals and in foams. A further generalization of these methods by and , known as the cellular Potts model, has been used to simulate static and kinetic phenomena in foam and biological morphogenesis. (Wikipedia).

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http://www.mekanizmalar.com/menu_engine.html

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Related pages

Temperature | Chromatic polynomial | Fixed point (mathematics) | Hamiltonian mechanics | Lattice (group) | Gibbs state | Kronecker delta | Wetting | Base (topology) | Boltzmann constant | Transfer operator | Markov chain Monte Carlo | Spin (physics) | Non-abelian group | Tutte polynomial | Percolation theory | Cylinder set | Cellular Potts model | Adjacency matrix | Phase transition | Z N model | Closed-form expression | Euclidean space | Subshift of finite type | Probability measure | Partition function (statistical mechanics) | Shift operator | Random cluster model | Ising model | Measure (mathematics) | P-adic number | Cardinality | Minimal model (physics) | Circle | Product topology