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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.
What are the dynamics of the Potts model?
Specialized to the Potts model: IUpdate sites via IID Poisson(1) clocks IAn update at x 2V replaces ˙(x)by a new spin ˘\ p(˙(x) 2j˙\ Vnfxg). e3 1 1 e Meta question: How long does it take to converge to \? E. Lubetzky 4 Glauber dynamics for the Potts model Recall: \(˙) = 1 Zp exp \ X x˘y 1f ˙(x)= y)g
How did Potts come up with the XY model?
Potts provided the location in two dimensions of the phase transition, for q = 3 and 4. In the limit as q → ∞, this becomes the XY model . What is now known as the standard Potts model was suggested by Potts in the course of his study above, and uses a simpler Hamiltonian, given by:
What kind of lattice does the Potts model use?
The Potts model consists of spins that are placed on a lattice; the lattice is usually taken to be a two-dimensional rectangular Euclidean lattice, but is often generalized to other dimensions or other lattices. Domb originally suggested that the spin takes one of q possible values, distributed uniformly about the circle, at angles
Which is a generalization of the Potts model?
Generalizations of the Potts model have also been used to model grain growth in metals and coarsening in foams. A further generalization of these methods by James Glazier and Francois Graner, known as the cellular Potts model, has been used to simulate static and kinetic phenomena in foam and biological morphogenesis .
How does the Q state Potts model work?
The q -state Potts models are generalizations of the 2-d Ising model, which can be taken to be the case of q = 2. In the q -state Potts model each spin may be found to be oriented in q possible directions and interacts with its neighbors via a Kroneker δ-function interaction.
Anthony Rollett, in Recrystallization and Related Annealing Phenomena (Third Edition), 2017