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 |
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 ⓘ |
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