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 14:20, 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, 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 S=1,2, \cdots, q } .
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 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
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)