Editing Conformal symmetry (section)

== Mathematical proofs of conformal invariance in lattice models ==

Physicists have found that many lattice models become conformally invariant in the critical limit. However, mathematical proofs of these results have only appeared much later, and only in some cases.

In 2010, the mathematician [[Stanislav Smirnov]] was awarded the [[Fields medal]] "for the proof of [[conformally invariant|conformal invariance]] of [[percolation theory|percolation]] and the planar [[Ising model]] in statistical physics".<ref name="fields_profile">{{Cite web|url=http://www.icm2010.org.in/wp-content/icmfiles/uploads/Stanislav_Smirnov_profile1.pdf|title=Stanislav Smirnov profile|last=Rehmeyer|first=Julie|date=19 August 2010|publisher=[[International Congress of Mathematicians]]|accessdate=19 August 2010|archive-date=7 March 2012|archive-url=https://web.archive.org/web/20120307020115/http://www.icm2010.org.in/wp-content/icmfiles/uploads/Stanislav_Smirnov_profile1.pdf|url-status=dead}}</ref>

In 2020, the mathematician [[Hugo Duminil-Copin]] and his collaborators proved that [[rotational invariance]] exists at the boundary between phases in many physical systems.<ref>{{Cite magazine|title=Mathematicians Prove Symmetry of Phase Transitions|language=en-US|magazine=Wired|url=https://www.wired.com/story/mathematicians-prove-symmetry-of-phase-transitions/|access-date=2021-07-14|issn=1059-1028}}</ref><ref>{{cite arXiv|last1=Duminil-Copin|first1=Hugo|last2=Kozlowski|first2=Karol Kajetan|last3=Krachun|first3=Dmitry|last4=Manolescu|first4=Ioan|last5=Oulamara|first5=Mendes|date=2020-12-21|title=Rotational invariance in critical planar lattice models|class=math.PR|eprint=2012.11672}}</ref>