Reference

Citation cross-reference: look up a model by author name, year, or physical keyword. Search this page (Ctrl+F) to find the QAtlas entry for a physical system you have in mind.

Classical Models

ModelKey References
BCFTCardy1989, AffleckLudwig1991, FriedanKonechny2004
ConformalBootstrapKosPolandSimmonsDuffin2014, Kos2016, SimmonsDuffin2017, Reehorst2021
IsingChain1DIsing1925, Brush1967
LiouvilleCFTPolyakov1981, ZamolodchikovZamolodchikov1996
LogarithmicCFTSaleur1992, Cardy2001, PearceRasmussenZuber2006, VasseurJacobsenSaleur2011
RFIMImryMa1975, Imbrie1985, BricmontKupiainen1987
RandomBondIsing2DEdwardsAnderson1975, Nishimori1981, HoneckerPiccoPujol2001
SLEkappaSchramm2000, BauerBernard2006, Cardy2005, Beffara2008
SherringtonKirkpatrickSherringtonKirkpatrick1975, Parisi1980, CrisantiRizzo2002, Talagrand2006
SpinIcePauling1935
TTbarZamolodchikov2004, SmirnovZamolodchikov2017, CavagliaNegroSzecsenyiTateo2016
TodaLatticeToda1967, Flaschka1974

Quantum Models

ModelKey References
AKLT1DAKLT1988, KennedyTasaki1992, GarciaSaez2013, Arovas1988, Lohmann2014, Lou2000
AKLT2DAKLT1988, VerstraeteCirac2004
ChernSimons3DWitten1989, KnizhnikZamolodchikov1984, Verlinde1988
Cluster1DBriegelRaussendorf2001
Compass1DBrzezickiDziarmagaOles2007, KugelKhomskii1982, Kitaev2006
DMIHeisenberg1DHulthen1938, Dzyaloshinsky1958, Moriya1960, AffleckOshikawa1999
ExtendedHubbard1DLiebWu1968, Voit1995, Nakamura2000
FibonacciAnyonsFreedmanKitaevLarsenWang2003, ReadRezayi1999, KitaevPreskill2006
GrossNeveuGrossNeveu1974, AndreiLowenstein1979
HeisenbergXYZYangYang1966, LiebSchultzMattis1961, Baxter1972, LutherPeschel1975, McCoyWu1978
TightBinding(Honeycomb)
Hubbard1DLiebWu1968, Essler2005, Ovchinnikov1970, Voit1995, JuttnerKlumperSuzuki1998
J1J2Heisenberg1DHulthen1938, MajumdarGhosh1969, WhiteAffleck1996
TightBinding(Kagome)
KagomeHeisenbergAFMYanHuseWhite2011, DepenbrockMcCullochSchollwock2012, IqbalBeccaSorellaPoilblanc2013, KitaevPreskill2006, LevinWen2006, JiangWangBalents2012
KitaevHeisenbergKitaev2006, RauLeeKee2014
KitaevHoneycombKitaev2006, Lieb1994
TightBinding(Lieb)
LongRangeIsing1DPfeuty1970, KoffelLewensteinTagliacozzo2012, GongFossFeig2014
LongRangeXY1DLiebSchultzMattis1961, Pfeuty1970, MaghrebiGongGorshkov2017
MajumdarGhoshMajumdarGhosh1969, ShastrySutherland1981, WhiteAffleck1996, Eggert1996
MixedFieldIsing1DPfeuty1970, McCoyWu1978
PXP1DTurnerMichailidisAbaninSerbynPapic2018, LinMotrunich2019, IadecolaSchecterXu2019, Surace2020
PpIp2DSCReadGreen2000, Kitaev2006
S1AnisotropicD1DWhiteHuse1993, ChenHidaSanctuary2003, TzengYang2008
S1Heisenberg1DWhiteHuse1993
S1XXZ1DWhiteHuse1993, Schulz1986, TzengYang2008
SYKSachdevYe1993, Kitaev2015, MaldacenaStanford2016
SchwingerModelSchwinger1962, ColemanJackiwSusskind1975
ShastrySutherlandShastrySutherland1981, KogaKawakami2000
TightBinding1DAshcroftMermin1976, Mahan2000, Coleman2015, Korringa1950
TightBindingV1DYangYang1966, AshcroftMermin1976, Mahan2000, Coleman2015
ToricCodeKitaev2003, KitaevPreskill2006, LevinWen2006, NayakSimonSternFreedmanDasSarma2008
TightBinding(Triangular)
XCubeVijayHaahFu2016, SlagleKim2017
XYh1DLiebSchultzMattis1961, Pfeuty1970

Other

ModelKey References
BoundMaldacenaShenkerStanford2016, MargolusLevitin1998, MandelstamTamm1945, SekinoSusskind2008, Bekenstein1981, CHSH1969, Tsirelson1980, PopescuRohrlich1994, Mermin1990, BuzekHillery1996, ShorPreskill2000
CurieWeissIsingLandauLifshitz1980, Landau1937, Stanley1971
DimerLatticeKasteleyn1961, TemperleyFisher1961, Fisher1961
HaldaneShastryHaldane1988, Shastry1988, Affleck1986, CalabreseCardy2004
Heisenberg1DHulthen1938, Bethe1931, desCloizeauxPearson1962, MullerThomasBeckBonner1981, Karbach1997, LutherPeschel1975, Affleck1989, Haldane1980, Affleck1986, BloteCardyNightingale1986, EggertAffleckTakahashi1994, CalabreseCardy2004, Cardy1986
IsingSquareOnsager1944, Yang1952
IsingTriangularWannier1950, Houtappel1950, Onsager1944, Baxter1982
Kitaev1DKitaev2001, Alicea2012, AsbothOroszlanyPalyi2016
SSHSSH1979, AsbothOroszlanyPalyi2016, SSH1980
SixVertexLieb1967a, Lieb1967b, Sutherland1967, Baxter1982, Lieb1967c
TASEPKardarParisiZhang1986, DerridaEvansHakimPasquier1993, DerridaLebowitz1998
TFIMPfeuty1970, BelavinPolyakovZamolodchikov1984, Sachdev1997, BarouchMcCoy1970, CalabreseEsslerFagotti2012, Peschel2003, LiebSchultzMattis1961, Sachdev2011, CalabreseCardy2009, CalabreseCardy2004, Heyl2013, Heyl2018, Rigol2007, CalabreseCardy2005, Gu2010, Damski2013, Onsager1944, LiebRobinson1972, HastingsKoma2006, Cardy1986, BloteCardyNightingale1986
TricriticalIsingBelavinPolyakovZamolodchikov1984, FriedanQiuShenker1984
TricriticalPotts3AndrewsBaxterForrester1984, Huse1984, BelavinPolyakovZamolodchikov1984
UniversalityCardy1986, BloteCardyNightingale1986, Affleck1986
XXZ1DYangYang1966, Takahashi1999, Hulthen1938, Giamarchi2003, desCloizeauxPearson1962, ChitraGiamarchi1997, Mahan2000, Coleman2015, Klumper1993, CalabreseEsslerFagotti2012, Heyl2013, EsslerFagotti2016, YangYang1969, CalabreseCardy2004, PerezCastillo2020
YangLeeCardy1984, YangLee1952
ZnClockJoseKadanoffKirkpatrickNelson1977, ElitzurPearsonShigemitsu1979
ZnParafermionFateevZamolodchikov1985