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 [math]\displaystyle{ J_1 }[/math] represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and [math]\displaystyle{ J_2 }[/math] represents the exchange interaction to the next nearest-neighbor.

[math]\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 }[/math]

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): 184420. 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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