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.

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

${\displaystyle {\hat {H}}=J_{1}\sum _{\langle ij\rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}+J_{2}\sum _{\langle \langle ij\rangle \rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}}$

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

• 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.
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