• Source: 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




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


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. 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.

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