Potts model

The Potts model was proposed by Renfrey B. Potts in 1952 (Ref. 1). The Potts model is a generalisation of the Ising model to more than two components.

For a general discussion on Potts models see Ref.2.

In practice one has a lattice system. The sites of the lattice can be occupied by particles of different species, $S=1,2,\cdots ,q$.

The energy of the system, $E$, is defined as:

$E=-K\sum _{<ij>}\delta (S_{i},S_{j})$

where $K$ is the coupling constant, $<ij>$ indicates that the sum is done exclusively over pairs of nearest neighbor sites, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta(S_i,S_j) } is the Kronecker delta.

The particular case Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=2 } is equivalent to the Ising model

See also

• Ashkin-Teller model
• Kac model

References

1. Renfrey B. Potts "Some generalized order-disorder transformations", Proceedings of the Cambridge Philosophical Society 48 pp. 106−109 (1952)
2. F. Y. Wu "The Potts model", Reviews of Modern Physics 54 pp. 235-268 (1982)
3. F. Y. Wu "Erratum: The Potts model", Reviews of Modern Physics 55 p. 315 (1983)