Heisenberg model

E107439

lattice model model in quantum magnetism quantum spin model theoretical framework in condensed matter physics

The Heisenberg model is a fundamental theoretical framework in quantum mechanics and condensed matter physics that describes interacting spins on a lattice and underpins much of our understanding of magnetism in materials.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (7)

Label	Occurrences
Heisenberg model canonical	6
Heisenberg spin chain	2
Heisenberg ferromagnet	1
XXX Heisenberg model	1
classical Heisenberg model	1
isotropic Heisenberg model	1
quantum Heisenberg model	1

Statements (50)

Predicate	Object
instanceOf	lattice model ⓘ model in quantum magnetism ⓘ quantum spin model ⓘ theoretical framework in condensed matter physics ⓘ
appliesTo	insulating magnetic crystals ⓘ low-dimensional quantum magnets ⓘ transition metal oxides ⓘ
assumes	short-range interactions between neighboring spins ⓘ spins located on lattice sites ⓘ
basedOn	exchange interaction ⓘ spin–spin interaction ⓘ
capturesPhenomenon	magnons ⓘ spin waves ⓘ
coreConceptIn	quantum many-body physics ⓘ theory of magnetism ⓘ
describes	interacting spins on a lattice ⓘ quantum magnetism in materials ⓘ
field	condensed matter physics ⓘ quantum mechanics ⓘ statistical mechanics ⓘ
generalizedBy	frustrated spin models ⓘ t–J model ⓘ
hasHamiltonianForm	H = ∑_{⟨i,j⟩} J_{ij} S_i · S_j ⓘ
hasVariant	Heisenberg antiferromagnet ⓘ Heisenberg model self-linksurface differs ⓘ surface form: Heisenberg ferromagnet XY model ⓘ surface form: XX Heisenberg model Heisenberg model self-linksurface differs ⓘ surface form: XXX Heisenberg model XXZ spin chain ⓘ surface form: XXZ Heisenberg model anisotropic Heisenberg model ⓘ Heisenberg model self-linksurface differs ⓘ surface form: classical Heisenberg model Heisenberg model self-linksurface differs ⓘ surface form: isotropic Heisenberg model Heisenberg model self-linksurface differs ⓘ surface form: quantum Heisenberg model
includesOperator	spin operator S_i ⓘ
includesParameter	exchange constant J ⓘ
namedAfter	Werner Heisenberg ⓘ
originatedIn	early 20th century ⓘ
relatedTo	Hubbard model ⓘ Ising models ⓘ surface form: Ising model XY model ⓘ
solvableInSpecialCase	one-dimensional spin-1/2 chain ⓘ
solvedBy	Bethe ansatz in one dimension ⓘ
supportsPhase	antiferromagnetic order ⓘ ferromagnetic order ⓘ paramagnetic phase ⓘ
usedFor	describing exchange interactions between spins ⓘ modeling magnetic ordering in solids ⓘ studying low-dimensional magnetism ⓘ studying phase transitions in magnetic systems ⓘ studying quantum spin chains ⓘ studying quantum spin liquids ⓘ

Referenced by (13)

Full triples — surface form annotated when it differs from this entity's canonical label.

Werner Heisenberg → notableWork → Heisenberg model ⓘ

Ising models → generalization → Heisenberg model ⓘ

subject surface form: Ising model

Bethe ansatz → solves → Heisenberg model ⓘ

this entity surface form: Heisenberg spin chain

Bethe ansatz → introducedFor → Heisenberg model ⓘ