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.


 * $$\hat H = J_1 \sum_{\langle ij \rangle}\vec S_i \cdot \vec S_j + J_2 \sum_{\langle\langle ij \rangle\rangle} \vec S_i \cdot \vec S_j $$