Editing Potts model (section)

{{short description|Model in statistical mechanics generalizing the Ising model}}
In [[statistical mechanics]], the '''Potts model''', a generalization of the [[Ising model]], is a model of interacting [[Spin (physics)|spins]] on a [[crystalline lattice]].<ref>{{Cite journal |last=Wu |first=F. Y. |date=1982-01-01 |title=The Potts model |url=https://link.aps.org/doi/10.1103/RevModPhys.54.235 |journal=Reviews of Modern Physics |volume=54 |issue=1 |pages=235–268 |doi=10.1103/RevModPhys.54.235|bibcode=1982RvMP...54..235W }}</ref> By studying the Potts model, one may gain insight into the behaviour of [[ferromagnet]]s and certain other phenomena of [[solid-state physics]].  The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is [[exactly solvable]], and that it has a rich mathematical formulation that has been studied extensively.

The model is named after [[Renfrey Potts]], who described the model near the end of his 1951 Ph.D. thesis.<ref>{{Cite journal |last1=Potts |first1=R. B. | authorlink1=Renfrey Potts |date=January 1952 |title=Some generalized order-disorder transformations |url=https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/some-generalized-orderdisorder-transformations/5FD50240095F40BD123171E5F76CDBE0 |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |language=en |volume=48 |issue=1 |pages=106–109 |doi=10.1017/S0305004100027419 |bibcode=1952PCPS...48..106P |s2cid=122689941 |issn=1469-8064}}</ref> The model was related to the "planar Potts" or "[[Z N model|clock model]]", which was suggested to him by his advisor, [[Cyril Domb]]. The four-state Potts model is sometimes known as the '''Ashkin–Teller model''',<ref>{{Cite journal |last1=Ashkin |first1=J. |last2=Teller |first2=E. |date=1943-09-01 |title=Statistics of Two-Dimensional Lattices with Four Components |url=https://link.aps.org/doi/10.1103/PhysRev.64.178 |journal=Physical Review |volume=64 |issue=5–6 |pages=178–184 |doi=10.1103/PhysRev.64.178|bibcode=1943PhRv...64..178A }}</ref> after [[Julius Ashkin]] and [[Edward Teller]], who considered an equivalent model in 1943.

The Potts model is related to, and generalized by, several other models, including the [[XY model]], the [[Heisenberg model (classical)|Heisenberg model]] and the [[N-vector model]]. The infinite-range Potts model is known as the [[Kac model]]. When the spins are taken to interact in a [[non-abelian group|non-Abelian]] manner, the model is related to the [[flux tube model]], which is used to discuss [[Color confinement|confinement]] in [[quantum chromodynamics]]. Generalizations of the Potts model have also been used to model [[grain growth]] in metals, [[coarsening]] in [[foam]]s, and statistical properties of [[Protein structure prediction|proteins]].<ref name=":1" /> A further generalization of these methods by [[James Glazier]] and [[Francois Graner]], known as the [[cellular Potts model]],<ref>{{Cite journal |last1=Graner |first1=François |last2=Glazier |first2=James A. |date=1992-09-28 |title=Simulation of biological cell sorting using a two-dimensional extended Potts model |url=https://link.aps.org/doi/10.1103/PhysRevLett.69.2013 |journal=Physical Review Letters |volume=69 |issue=13 |pages=2013–2016 |doi=10.1103/PhysRevLett.69.2013|pmid=10046374 |bibcode=1992PhRvL..69.2013G }}</ref> has been used to simulate static and kinetic phenomena in foam and biological [[morphogenesis]].