Ising models
E46143
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.
All labels observed (12)
How this entity was disambiguated
This entity first appeared as the object of triple T364219 — 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: Ising models Context triple: [Boltzmann machines, relatedTo, Ising models]
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A.
Journal of Statistical Physics
Journal of Statistical Physics is a peer-reviewed scientific journal focusing on research in statistical mechanics and related areas of theoretical physics.
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B.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
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C.
soft matter physics
Soft matter physics is the branch of physics that studies materials such as polymers, colloids, gels, liquid crystals, and biological matter, focusing on their complex structural, dynamical, and rheological properties.
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D.
Ginzburg–Landau theory of superconductivity
The Ginzburg–Landau theory of superconductivity is a phenomenological framework that describes superconductors using a complex order parameter and macroscopic equations to capture phase transitions, coherence length, and magnetic behavior.
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E.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
- 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: Ising models Target entity description: 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.
-
A.
Journal of Statistical Physics
Journal of Statistical Physics is a peer-reviewed scientific journal focusing on research in statistical mechanics and related areas of theoretical physics.
-
B.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
-
C.
soft matter physics
Soft matter physics is the branch of physics that studies materials such as polymers, colloids, gels, liquid crystals, and biological matter, focusing on their complex structural, dynamical, and rheological properties.
-
D.
Ginzburg–Landau theory of superconductivity
The Ginzburg–Landau theory of superconductivity is a phenomenological framework that describes superconductors using a complex order parameter and macroscopic equations to capture phase transitions, coherence length, and magnetic behavior.
-
E.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
- F. None of above. chosen
Statements (56)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
ⓘ
statistical mechanics model ⓘ |
| canInclude | long-range interactions ⓘ |
| computationalComplexity | NP-hard for general graphs ⓘ |
| describes |
interacting binary variables
ⓘ
spins on a lattice ⓘ |
| equivalentTo | binary Markov random field ⓘ |
| exactSolution | two-dimensional zero-field case ⓘ |
| exactSolutionBy | Lars Onsager ⓘ |
| field |
condensed matter physics
ⓘ
machine learning ⓘ probability theory ⓘ statistical mechanics ⓘ |
| generalization |
Heisenberg model
ⓘ
Potts model ⓘ spin glass models ⓘ |
| HamiltonianForm | H = -∑_{⟨i,j⟩} J_{ij} s_i s_j - ∑_i h_i s_i ⓘ |
| interactionParameter | J_{ij} ⓘ |
| interactionType | nearest-neighbor interaction ⓘ |
| localFieldParameter | h_i ⓘ |
| namedAfter | Ernst Ising ⓘ |
| noFiniteTemperatureTransition | one dimension ⓘ |
| OnsagerSolutionYear | 1944 ⓘ |
| parameter | inverse temperature β ⓘ |
| partitionFunctionSymbol | Z ⓘ |
| phaseTransitionDimension |
three dimensions
ⓘ
two dimensions ⓘ |
| probabilityDistributionForm | P(s) ∝ exp(-βH(s)) ⓘ |
| proposedBy | Wilhelm Lenz ⓘ |
| relatedConcept |
Curie temperature
ⓘ
linked to:
Curie point (Curie temperature)
critical exponents ⓘ spontaneous magnetization ⓘ universality class ⓘ |
| relatedOptimizationFormulation | quadratic unconstrained binary optimization ⓘ |
| representation | graphical model ⓘ |
| spinValues |
+1
ⓘ
-1 ⓘ |
| spinVariableSymbol | s_i ⓘ |
| typicalLattice |
one-dimensional lattice
ⓘ
three-dimensional lattice ⓘ two-dimensional lattice ⓘ |
| usedFor |
Boltzmann machine design
ⓘ
Markov random fields ⓘ combinatorial optimization ⓘ image denoising ⓘ probabilistic graphical modeling ⓘ quantum annealing formulations ⓘ study of critical phenomena ⓘ study of ferromagnetism ⓘ study of phase transitions ⓘ |
| usedIn |
computational biology
ⓘ
neuroscience network modeling ⓘ social interaction models ⓘ |
| variableType | binary spin ⓘ |
| yearAnalyzedByIsing | 1924 ⓘ |
| yearProposed | 1920 ⓘ |
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: Ising models Description of subject: 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.
Referenced by (31)
Full triples — surface form annotated when it differs from this entity's canonical label.
Lars Onsager
→
notableWork
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Crystal statistics. I. A two-dimensional model with an order-disorder transition
ⓘ
linked to: Ising models
subject linked to:
Hopfield networks
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Hopfield networks
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subject linked to:
Curie point (Curie temperature)
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subject linked to:
textbook "Statistical Mechanics"
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linked to: Ising models