J1 J2 model explained

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

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.\hat H = J _{1} \sum _{\langle} \vec S _{i} ⋅ \vec S _{j} + J _{2} \sum _{\langle\langle} \vec S _{i} ⋅ \vec 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.. J1−J2model: First-order phase transition versus deconfinement of spinons. Physical Review B. 73. 18. 2006. 184420 . 1098-0121. 10.1103/PhysRevB.73.184420. cond-mat/0601183. 54172992 .
• Ceccatto. H. A.. Gazza. C. J.. Trumper. A. E.. J1-J2model: Energy, correlations, and order-parameter fluctuations on finite lattices. Physical Review B. 45. 14. 1992. 7832–7836. 0163-1829. 10.1103/PhysRevB.45.7832.
• Dagotto. Elbio. Moreo. Adriana. Adriana Moreo . Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in 2 dimensions. Physical Review Letters. 63. 19. 1989. 2148–2151. 0031-9007. 10.1103/PhysRevLett.63.2148.
• Majumdar. Chanchal K.. Ghosh. Dipan K.. On Next‐Nearest‐Neighbor Interaction in Linear Chain. I. Journal of Mathematical Physics. 10. 8. 1969. 1388–1398. 0022-2488. 10.1063/1.1664978.
• Majumdar. Chanchal K.. Ghosh. Dipan K.. On Next‐Nearest‐Neighbor Interaction in Linear Chain. II. Journal of Mathematical Physics. 10. 8. 1969. 1399–1402. 0022-2488. 10.1063/1.1664979.