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The '''Potts model''' | 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 Refs. 2 and 3. | ||
In practice one has a lattice system. The sites of the lattice can be occupied by | 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>. | particles of different ''species'', <math> S=1,2, \cdots, q </math>. | ||
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the Potts model exhibits order-disorder [[phase transitions]]. For space dimensionality <math> d=2 </math>, and low values of <math> q </math> the transitions are continuous (<math> E(T) </math> is a continuous function), but the [[heat capacity]], <math> C(T) = (\partial E/\partial T) </math>, diverges at the transition [[temperature]]. The critical behaviour of | the Potts model exhibits order-disorder [[phase transitions]]. For space dimensionality <math> d=2 </math>, and low values of <math> q </math> the transitions are continuous (<math> E(T) </math> is a continuous function), but the [[heat capacity]], <math> C(T) = (\partial E/\partial T) </math>, diverges at the transition [[temperature]]. The critical behaviour of | ||
different values of <math> q </math> belong to (or define) different [[universality classes]] of criticality | different values of <math> q </math> belong to (or define) different [[universality classes]] of criticality | ||
For space dimensionality <math> d=3 </math>, the transitions for <math> q \ge 3 </math> are [[First-order transitions |first order]] (<math> E </math> shows a discontinuity at the transition temperature). | For space dimensionality <math> d=3 </math>, the transitions for <math> q \ge 3 </math> are [[First-order transitions |first order]] (<math> E </math> shows a discontinuity at the transition temperature). | ||
==See also== | ==See also== | ||
*[[Ashkin-Teller model]] | *[[Ashkin-Teller model]] | ||
*[[Kac model]] | *[[Kac model]] | ||
==References== | ==References== | ||
#Renfrey B. Potts "Some generalized order-disorder transformations", Proceedings of the Cambridge Philosophical Society '''48''' pp. 106−109 (1952) | |||
''' | #[http://dx.doi.org/10.1103/RevModPhys.54.235 F. Y. Wu "The Potts model", Reviews of Modern Physics '''54''' pp. 235-268 (1982)] | ||
#[http://dx.doi.org/10.1103/RevModPhys.55.315 F. Y. Wu "Erratum: The Potts model", Reviews of Modern Physics '''55''' p. 315 (1983)] | |||
# Rodney J. Baxter "Exactly Solved Models in Statistical Mechanics", Academic Press (1982) ISBN 0120831821 Chapter 12 (freely available [http://tpsrv.anu.edu.au/Members/baxter/book/Exactly.pdf pdf]) | |||
[[category:models]] | [[category:models]] |