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Angular momentum operator

Spin angular momentum

Heisenberg model

{c}

For $N$ spin-one-half systems and one term per unordered pair,
$$
\sum_{i<j}\boldsymbol\sigma_i\mathbin{\cdot}\boldsymbol\sigma_j
=2\mathbf S^2-\frac{3N}{2},
\qquad
\mathbf S=\frac12\sum_i\boldsymbol\sigma_i.
$$
Its minimum lies in the smallest available total-spin sector.

All-to-all Heisenberg model

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 343 / 2 / b / Solution

All-to-all Heisenberg model

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All-to-all Heisenberg model

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