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1. Exchange Interaction

   Linked via "exchange tensor"

   Empirical Measurement and Tensor Forms
   While the fundamental exchange interaction is a scalar quantity in the Heisenberg model, real systems often require a more complex, anisotropic description, especially when crystal field effects are significant. This leads to the generalized exchange tensor ($\mathbf{J}_{ij}$):
   $$H{\text{Generalized}} = -\sum{i \neq j} \mathbf{S}i \cdot \mathbf{J}{ij} \cdot \mathbf{S}_…