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For strings labeled by the positive integers, string-nets are the [[spin network]]s studied in [[loop quantum gravity]]. This has led to the proposal by Levin and Wen,<ref>{{cite journal |title=Photons and electrons as emergent phenomena |first1=Michael |last1=Levin |first2=Xiao-Gang |last2=Wen |journal=Rev. Mod. Phys. |volume=77 |pages=871–879 [878] |date=2005 |issue=3 |quote=loop quantum gravity appears to be a string net condensation ... |doi=10.1103/RevModPhys.77.871 |arxiv=cond-mat/0407140 |bibcode=2005RvMP...77..871L |s2cid=117563047 }}</ref> and Smolin, Markopoulou and Konopka<ref>{{cite arXiv |eprint=hep-th/0611197 |quote=We argue (but do not prove) that under certain conditions the spins in the system can arrange themselves in regular, lattice-like patterns at low temperatures. |first1=Tomasz |last1=Konopka |first2=Fotini |last2=Markopoulou |first3=Lee |last3=Smolin |title=Quantum Graphity |date=2006}}</ref> that loop quantum gravity's spin networks can give rise to the [[standard model]] of [[particle physics]] through this mechanism, along with [[fermi statistics]] and [[gauge bosons|gauge interactions]]. To date, a rigorous derivation from LQG's spin networks to Levin and Wen's spin lattice has yet to be done, but the project to do so is called [[quantum graphity]], and in a more recent paper, Tomasz Konopka, [[Fotini Markopoulou]], [[Simone Severini]] argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism.<ref>{{cite journal |title=Quantum graphity: A model of emergent locality |first1=Tomasz |last1=Konopka |first2=Fotini |last2=Markopoulou |first3=Simone |last3=Severini |journal=Phys. Rev. D |volume=77 |issue=10 |page=19 |date=May 2008 |doi=10.1103/PhysRevD.77.104029 |arxiv=0801.0861 |bibcode=2008PhRvD..77j4029K |s2cid=6959359 |quote=The characterization of the string-condensed ground state is difficult but its excitations are expected to be that of a U(1) gauge theory, ... The two main differences between this model and the original string-net condensation model proposed by Levin and Wen are that in the present case the background lattice is dynamical and has hexagonal rather than square plaquettes.}}</ref>
[[Herbertsmithite]] may be an example of string-net matter.<ref name=eureka>{{cite web|last=Bowles|first=Claire|title=Have researchers found a new state of matter?|url=http://www.eurekalert.org/pub_releases/2007-03/ns-hrf031407.php|publisher=Eureka Alert|accessdate=29 January 2012}}</ref><ref name=newscientist>{{cite journal|last=Merali|first=Zeeya|title=The universe is a string-net liquid|journal=New Scientist|date=2007-03-17|volume=193|issue=2595|pages=8–9|url=https://www.newscientist.com/article/mg19325954.200|accessdate=29 January 2012|doi=10.1016/s0262-4079(07)60640-x|url-access=subscription}}</ref>
==Examples==
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