Exchange interaction

Exchange interaction is an effective interaction arising from the indistinguishability of identical particles and the symmetry constraints on their quantum states. It can produce energy differences between states even without a corresponding classical force.

Pauli exclusion principle: No two identical fermions can occupy the same quantum state. Its restriction on fermion states underlies exchange effects in electrons.
Exchange energy: An energy contribution arising from overlap and exchange symmetry of identical-particle wavefunctions. It quantifies the energetic splitting generated by exchange interaction.
Coulomb interaction: The electrostatic interaction between electric charges, described by Coulomb's law. It is a direct force, unlike exchange's symmetry-based energy contribution.
Heisenberg model: A lattice model describing interacting spins through pairwise spin couplings. Its effective coupling constants compress complicated exchange processes into a solvable framework.
Spin-statistics theorem: A relativistic theorem linking particle spin to bosonic or fermionic exchange symmetry. It explains why identical electrons require antisymmetric states.
Ferromagnetism: A form of magnetism in which spontaneous ordering aligns magnetic moments. Positive effective exchange often favors parallel neighboring spins.
Dipole-dipole interaction: An interaction between spatially separated electric or magnetic dipoles. Its classical spatial mechanism differs from exchange coupling.
Hubbard model: A lattice model balancing electron hopping against local Coulomb repulsion. Exchange interactions emerge from its competing hopping and repulsion terms.
Slater determinant: An antisymmetric wavefunction construction used to describe multiple identical fermions. Antisymmetrizing electron states makes exchange terms appear in energy calculations.
Antiferromagnetism: Magnetic order in which neighboring moments align oppositely. Exchange can favor antiparallel spin alignment instead of parallel order.

Linked from 18 pages