J1 J2 model

The J1–J2 model is a quantum spin model like the Heisenberg model but also includes a term for the interaction between next-nearest neighbor spins.

## Hamiltonian

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In this model, the term  J 1 {\displaystyle J_{1}} represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and  J 2 {\displaystyle J_{2}} represents the exchange interaction to the next nearest-neighbor.

H ^ = J 1 ∑ ⟨ i j ⟩ S → i ⋅ S → j + J 2 ∑ ⟨ ⟨ i j ⟩ ⟩ S → i ⋅ S → j {\displaystyle {\hat {H}}=J_{1}\sum _{\langle ij\rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}+J_{2}\sum _{\langle \langle ij\rangle \rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}}

## See also

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

## References

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* Sirker, J.; Weihong, Zheng; Sushkov, O. P.; Oitmaa, J. (2006). "J1−J2model: First-order phase transition versus deconfinement of spinons". Physical Review B. 73 (18): 184420. arXiv:cond-mat/0601183. doi:10.1103/PhysRevB.73.184420. ISSN 1098-0121. S2CID 54172992.
* Ceccatto, H. A.; Gazza, C. J.; Trumper, A. E. (1992). "J1-J2model: Energy, correlations, and order-parameter fluctuations on finite lattices". Physical Review B. 45 (14): 7832–7836\. doi:10.1103/PhysRevB.45.7832. ISSN 0163-1829.
* Dagotto, Elbio; Moreo, Adriana (1989). "Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in 2 dimensions" (PDF). Physical Review Letters. 63 (19): 2148–2151\. doi:10.1103/PhysRevLett.63.2148. ISSN 0031-9007.
* Majumdar, Chanchal K.; Ghosh, Dipan K. (1969). "On Next‐Nearest‐Neighbor Interaction in Linear Chain. I". Journal of Mathematical Physics. 10 (8): 1388–1398\. doi:10.1063/1.1664978. ISSN 0022-2488.
* Majumdar, Chanchal K.; Ghosh, Dipan K. (1969). "On Next‐Nearest‐Neighbor Interaction in Linear Chain. II". Journal of Mathematical Physics. 10 (8): 1399–1402\. doi:10.1063/1.1664979. ISSN 0022-2488.