XY model
E450153
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| 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 NERFINISHED ⓘ |
| couplingConstantSymbol | J ⓘ |
| describes | two-dimensional spins with continuous symmetry ⓘ |
| exhibits | Kosterlitz–Thouless transition NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
understanding topological defects in 2D ⓘ |
| interactionType | nearest-neighbor spin coupling ⓘ |
| longRangeOrderIn2D | absent at finite temperature ⓘ |
| lowTemperaturePhase | quasi-long-range order ⓘ |
| obeys | Mermin–Wagner theorem NERFINISHED ⓘ |
| relatedTo |
Heisenberg model
ⓘ
Ising model NERFINISHED ⓘ 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: XY model Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
XX Heisenberg model