Bogoliubov inequality
E461417
The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bogoliubov inequality canonical | 1 |
| Peierls–Bogoliubov inequality | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4681195 — 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: Bogoliubov inequality Context triple: [Nikolay Bogolyubov, notableWork, Bogoliubov inequality]
-
A.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
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B.
Hardy inequality
The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
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C.
Lyapunov inequality
The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
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D.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
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E.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
- 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: Bogoliubov inequality Target entity description: The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
-
A.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
B.
Hardy inequality
The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
-
C.
Lyapunov inequality
The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
-
D.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
-
E.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical inequality
ⓘ
result in quantum field theory ⓘ result in statistical mechanics ⓘ |
| appliesTo |
classical spin systems
ⓘ
lattice models in statistical mechanics ⓘ quantum spin systems ⓘ |
| assumes |
thermal equilibrium state
ⓘ
well-defined Hamiltonian ⓘ |
| category |
inequalities in physics
ⓘ
tools for rigorous statistical mechanics ⓘ |
| concerns |
commutators of observables
ⓘ
correlation functions ⓘ thermal expectation values ⓘ |
| context |
equilibrium statistical mechanics
ⓘ
quantum many-body theory ⓘ |
| field |
mathematical physics
ⓘ
quantum field theory ⓘ statistical mechanics ⓘ |
| hasConsequence |
constraints on possible symmetry breaking patterns
ⓘ
restrictions on magnetization in spin models ⓘ |
| historicalPeriod | 20th century ⓘ |
| implies | bounds on long-range order ⓘ |
| language | operator formalism ⓘ |
| mathematicalForm | inequality between correlation functions and commutators ⓘ |
| namedAfter | Nikolay Bogoliubov NERFINISHED ⓘ |
| relatedTo |
Bogoliubov variational principle
NERFINISHED
ⓘ
Bogoliubov–Kubo–Mori inner product NERFINISHED ⓘ GKS inequalities NERFINISHED ⓘ Griffiths inequalities NERFINISHED ⓘ Mermin–Wagner theorem NERFINISHED ⓘ Peierls argument NERFINISHED ⓘ |
| requires |
Hilbert space framework
ⓘ
definition of thermal trace ⓘ |
| typicalModel |
Bose systems
ⓘ
Heisenberg model NERFINISHED ⓘ Ising-type models NERFINISHED ⓘ |
| use |
bounding correlation functions
ⓘ
deriving bounds on order parameters ⓘ proving existence of phase transitions in lattice models ⓘ rigorous analysis of phase transitions ⓘ studying spontaneous symmetry breaking ⓘ |
| usedBy |
condensed matter theorists
ⓘ
mathematical physicists ⓘ quantum field theorists ⓘ |
| usedIn |
analysis of low-dimensional systems
ⓘ
proofs of absence of phase transitions in some dimensions ⓘ rigorous theory of critical phenomena ⓘ |
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: Bogoliubov inequality Description of subject: The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Rudolf Peierls
this entity surface form:
Peierls–Bogoliubov inequality