Heisenberg model

The Heisenberg model couples neighboring or more general pairs of spins through ${\mathbf{\sigma }}_i\cdot {\mathbf{\sigma }}_j$. For all-to-all equal coupling, the Hamiltonian can be written in terms of the square of the total spin.

For $N$ spin-one-half systems and one term per unordered pair,Its minimum lies in the smallest available total-spin sector.