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

In this model, the term J1 represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and J2 represents the exchange interaction to the next nearest-neighbor.

H^=J1∑⟨ij⟩S→i⋅S→j+J2∑⟨⟨ij⟩⟩S→i⋅S→j

## See also

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

## References

* 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). doi:10.1103/PhysRevB.73.184420. ISSN 1098-0121.
* 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". Physical Review Letters 63 (19): 2148–2151. doi:10.1103/PhysRevLett.63.2148. ISSN 0031-9007. http://sces.phys.utk.edu/mostcited/mc15_1114.pdf.
* 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.

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