Editing Potts model
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
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>. | ||
Line 10: | Line 10: | ||
Note that the particular case <math> q=2 </math> is equivalent to the [[Ising Models | Ising model]]. | Note that the particular case <math> q=2 </math> is equivalent to the [[Ising Models | Ising model]]. | ||
==Phase | ===Phase transtions=== | ||
Considering a symmetric situation (i.e. equal | Considering a symmetric situation (i.e. equal chemical potential for all the species): | ||
<math> \mu_1 = \mu_2 = \cdots = \mu_q </math>; | |||
the Potts models exhibit 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 behavior 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 (<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)] | |||
[[category:models]] | [[category:models]] |