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.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| XX Heisenberg model | 1 |
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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
XX Heisenberg model