XY model

E450153

lattice model model in condensed matter physics model in statistical mechanics spin model

The XY model is a two-dimensional spin model in statistical mechanics and condensed matter physics where spins can rotate freely in a plane, used to study phase transitions and phenomena like the Kosterlitz–Thouless transition.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
O(N) models	1
XX Heisenberg model	1
XY model canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T4537415 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: XY model
Context triple: [Heisenberg model, relatedTo, XY model]

A. Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
B. Heisenberg model
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.
C. Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
D. Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
E. Nambu–Jona-Lasinio model
The Nambu–Jona-Lasinio model is a theoretical framework in quantum field theory that illustrates spontaneous chiral symmetry breaking and mass generation for fermions, analogous to mechanisms in superconductivity.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: XY model
Target entity description: The XY model is a two-dimensional spin model in statistical mechanics and condensed matter physics where spins can rotate freely in a plane, used to study phase transitions and phenomena like the Kosterlitz–Thouless transition.

A. Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
B. Heisenberg model
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.
C. Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
D. Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
E. Nambu–Jona-Lasinio model
The Nambu–Jona-Lasinio model is a theoretical framework in quantum field theory that illustrates spontaneous chiral symmetry breaking and mass generation for fermions, analogous to mechanisms in superconductivity.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	lattice model ⓘ model in condensed matter physics ⓘ model in statistical mechanics ⓘ spin model ⓘ
analyzedBy	Monte Carlo simulations ⓘ renormalization group methods ⓘ spin-wave approximation ⓘ
belongsToClass	O(N) models ⓘ linked to: XY model
couplingConstantSymbol	J ⓘ
describes	two-dimensional spins with continuous symmetry ⓘ
exhibits	Kosterlitz–Thouless transition ⓘ linked to: Kosterlitz–Thouless–Halperin–Nelson–Young theory
fieldTheoryLimit	compact scalar field theory ⓘ
hasAlternativeName	planar rotor model ⓘ planar spin model ⓘ
hasOrderParameter	complex magnetization ⓘ
hasSpinDegreesOfFreedom	O(2) symmetry ⓘ U(1) symmetry ⓘ
hasSymmetry	continuous global U(1) symmetry ⓘ
hasTopologicalExcitations	vortex–antivortex pairs ⓘ vortices ⓘ
highTemperaturePhase	disordered phase ⓘ
importantFor	Berezinskii–Kosterlitz–Thouless theory ⓘ linked to: Kosterlitz–Thouless–Halperin–Nelson–Young theory understanding topological defects in 2D ⓘ
interactionType	nearest-neighbor spin coupling ⓘ
longRangeOrderIn2D	absent at finite temperature ⓘ
lowTemperaturePhase	quasi-long-range order ⓘ
obeys	Mermin–Wagner theorem ⓘ linked to: Landau–Peierls instability
relatedTo	Heisenberg model ⓘ Ising model ⓘ linked to: Ising models clock model ⓘ sine-Gordon model ⓘ
specialCaseOf	O(N) model with N = 2 ⓘ
spinComponents	two ⓘ
spinMagnitude	fixed ⓘ
spinOrientation	continuous angle variable ⓘ
spinSpace	plane ⓘ
spinVariableSymbol	θ_i ⓘ
transitionTypeIn2D	topological phase transition ⓘ
typicalHamiltonianForm	H = -J Σ⟨ij⟩ cos(θ_i - θ_j) ⓘ
typicalLatticeDimension	two-dimensional ⓘ
usedIn	study of Josephson junction arrays ⓘ study of Kosterlitz–Thouless transition ⓘ study of critical phenomena ⓘ study of phase transitions ⓘ study of superfluid films ⓘ study of thin superconducting films ⓘ study of topological phase transitions ⓘ study of two-dimensional magnetism ⓘ study of vortex physics ⓘ

How these facts were elicited

Referenced by (3)

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

Heisenberg model → hasVariant → XX Heisenberg model ⓘ

linked to: XY model

Heisenberg model → relatedTo → XY model ⓘ

XY model → belongsToClass → O(N) models ⓘ