Editing 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
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_{ \langle ij \rangle } \delta (S_i,S_j) </math>
where <math> K </math> is the coupling constant, <math> \langle ij \rangle </math> indicates
that the sum is performed exclusively over pairs of nearest neighbour sites,  and <math> \delta(S_i,S_j) </math> is the [[Kronecker delta|Kronecker delta]].
Note that the particular case <math> q=2 </math> is equivalent to the [[Ising Models | Ising model]].

==Phase transitions==
Considering a symmetric situation (i.e. equal [[chemical potential]] for all the species):

:<math> \mu_1 = \mu_2 = \cdots = \mu_q </math>;

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

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==
*[[Ashkin-Teller model]]
*[[Kac model]]
==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]]