Potts model: Difference between revisions
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The '''Potts model''' was proposed by Renfrey B. Potts in 1952 (Ref. 1). The Potts model is a generalisation of the [[Ising Models | Ising model]] to more than two components. | The '''Potts model''' was proposed by Renfrey B. Potts in 1952 (Ref. 1). The Potts model is a generalisation of the [[Ising Models | 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''', <math> S=1,2, \cdots, q </math>. | |||
The energy of the system, <math> E </math>, is defined as: | |||
:<math> E = - K \sum_{<ij>} \delta (S_i,S_j) </math> | |||
where <math> K </math> is the coupling constant, <math> <ij> </math> indicates | |||
that the sum is done exclusively over pairs of nearest neighbor sites, and <math> \delta(S_i,S_j) </math> is the [[Kronecker delta|Kronecker delta]]. | |||
The particular case <math> q=2 </math> is equivalent to the [[Ising Models | Ising model]] | |||
==See also== | ==See also== | ||
*[[Ashkin-Teller model]] | *[[Ashkin-Teller model]] | ||
Revision as of 15:20, 4 July 2008
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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, .
The energy of the system, 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 E } , is defined as:
- 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 E = - K \sum_{<ij>} \delta (S_i,S_j) }
where 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 K } is the coupling constant, 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 <ij> } indicates that the sum is done exclusively over pairs of nearest neighbor sites, and 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
References
- Renfrey B. Potts "Some generalized order-disorder transformations", Proceedings of the Cambridge Philosophical Society 48 pp. 106−109 (1952)
- F. Y. Wu "The Potts model", Reviews of Modern Physics 54 pp. 235-268 (1982)
- F. Y. Wu "Erratum: The Potts model", Reviews of Modern Physics 55 p. 315 (1983)