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J1 J2 model

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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

References

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