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 $J_1$ represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and $J_2$ represents the exchange interaction to the next nearest-neighbor.

$\hat{H}=J_1\sum _{⟨ij⟩}{\overrightarrow{S}}_i\cdot {\overrightarrow{S}}_j+J_2\sum _{⟨⟨ij⟩⟩}{\overrightarrow{S}}_i\cdot {\overrightarrow{S}}_j$

See also

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