J1 J2 model

In this model, the term $J\_1$ represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and $J\_2$ represents the exchange interaction to the next nearest-neighbor.

: $\backslash hat\; H\; =\; J\_1\; \backslash sum\_\{\backslash langle\; ij\; \backslash rangle\}\backslash vec\; S\_i\; \backslash cdot\; \backslash vec\; S\_j\; +\; J\_2\; \backslash sum\_\{\backslash langle\backslash langle\; ij\; \backslash rangle\backslash rangle\}\; \backslash vec\; S\_i\; \backslash cdot\; \backslash vec\; S\_j$

• Spin model
• Heisenberg model (quantum)
• Hubbard model
• t-J model
• Majumdar–Ghosh model

• {{cite journal|last1=Sirker|first1=J.|last2=Weihong|first2=Zheng|last3=Sushkov|first3=O. P.|last4=Oitmaa|first4=J.|title=J1−J2model: First-order phase transition versus deconfinement of spinons|journal=Physical Review B|volume=73|issue=18|year=2006|page=184420 |issn=1098-0121|doi=10.1103/PhysRevB.73.184420|arxiv=cond-mat/0601183|s2cid=54172992 }}
• {{cite journal|last1=Ceccatto|first1=H. A.|last2=Gazza|first2=C. J.|last3=Trumper|first3=A. E.|title=J1-J2model: Energy, correlations, and order-parameter fluctuations on finite lattices|journal=Physical Review B|volume=45|issue=14|year=1992|pages=7832–7836|issn=0163-1829|doi=10.1103/PhysRevB.45.7832}}
• {{cite journal|last1=Dagotto|first1=Elbio|last2=Moreo|first2=Adriana|author2-link= Adriana Moreo |title=Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in 2 dimensions|journal=Physical Review Letters|volume=63|issue=19|year=1989|pages=2148–2151|issn=0031-9007|doi=10.1103/PhysRevLett.63.2148|url=http://sces.phys.utk.edu/mostcited/mc15_1114.pdf}}
• {{cite journal|last1=Majumdar|first1=Chanchal K.|last2=Ghosh|first2=Dipan K.|title=On Next‐Nearest‐Neighbor Interaction in Linear Chain. I|journal=Journal of Mathematical Physics|volume=10|issue=8|year=1969|pages=1388–1398|issn=0022-2488|doi=10.1063/1.1664978}}
• {{cite journal|last1=Majumdar|first1=Chanchal K.|last2=Ghosh|first2=Dipan K.|title=On Next‐Nearest‐Neighbor Interaction in Linear Chain. II|journal=Journal of Mathematical Physics|volume=10|issue=8|year=1969|pages=1399–1402|issn=0022-2488|doi=10.1063/1.1664979}}

Category:Spin models

Category:Quantum magnetism