Brillouin function
E675970
The Brillouin function is a mathematical function in statistical mechanics that describes the magnetization of a paramagnetic material as a function of temperature and applied magnetic field.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Brillouin function canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T7603295 — 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: Brillouin function Context triple: [Léon Brillouin, notableConcept, Brillouin function]
-
A.
Curie constant
The Curie constant is a material-specific proportionality factor that characterizes how a paramagnetic substance’s magnetic susceptibility varies inversely with temperature.
-
B.
Beta function
The Beta function is a special function in mathematics, closely related to the Gamma function, that arises in calculus, probability theory, and complex analysis, particularly in evaluating integrals and expressing various identities.
-
C.
Curie–Weiss law
The Curie–Weiss law is a refinement of Curie’s law in magnetism that accounts for magnetic interactions between atoms by introducing a characteristic temperature, improving the description of paramagnetic susceptibility near ferromagnetic phase transitions.
-
D.
Du Bois-Reymond function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
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E.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
- 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: Brillouin function Target entity description: The Brillouin function is a mathematical function in statistical mechanics that describes the magnetization of a paramagnetic material as a function of temperature and applied magnetic field.
-
A.
Curie constant
The Curie constant is a material-specific proportionality factor that characterizes how a paramagnetic substance’s magnetic susceptibility varies inversely with temperature.
-
B.
Beta function
The Beta function is a special function in mathematics, closely related to the Gamma function, that arises in calculus, probability theory, and complex analysis, particularly in evaluating integrals and expressing various identities.
-
C.
Curie–Weiss law
The Curie–Weiss law is a refinement of Curie’s law in magnetism that accounts for magnetic interactions between atoms by introducing a characteristic temperature, improving the description of paramagnetic susceptibility near ferromagnetic phase transitions.
-
D.
Du Bois-Reymond function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
-
E.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
function in statistical mechanics
ⓘ
mathematical function ⓘ special function ⓘ |
| appliesTo |
dilute magnetic ions in crystals
ⓘ
localized spin systems ⓘ paramagnetic salts ⓘ |
| argument |
ratio of magnetic energy to thermal energy
ⓘ
x = g μ_B J B / (k_B T) ⓘ |
| assumes | non-interacting magnetic moments ⓘ |
| dependsOn |
applied magnetic field
ⓘ
temperature ⓘ total angular momentum quantum number J ⓘ |
| describes | magnetization of a paramagnetic material ⓘ |
| domain | real numbers ⓘ |
| expressedInTermsOf | hyperbolic cotangent functions ⓘ |
| field |
condensed matter physics
ⓘ
statistical mechanics ⓘ |
| hasFormula | B_J(x) = (2J+1)/(2J) coth[(2J+1)x/(2J)] - (1/(2J)) coth[x/(2J)] ⓘ |
| isMonotonic | true ⓘ |
| isOddFunction | true ⓘ |
| limitCase |
linear in x for small x
ⓘ
reduces to Langevin function for J → ∞ ⓘ
linked to:
Langevin function
saturates to -1 for large negative x ⓘ saturates to 1 for large positive x ⓘ |
| namedAfter | Léon Brillouin ⓘ |
| parameter |
Bohr magneton μ_B
ⓘ
linked to:
Bohr magneton
Boltzmann constant k_B ⓘ
linked to:
k_B
Landé g-factor ⓘ absolute temperature T ⓘ magnetic field B ⓘ |
| range | [-1, 1] ⓘ |
| relatedConcept |
Curie law
ⓘ
linked to:
Curie law of magnetization
Curie–Weiss law ⓘ magnetic susceptibility ⓘ |
| relatedTo | Langevin function ⓘ |
| usedFor |
description of Langevin paramagnetism generalization
ⓘ
magnetization curves of paramagnets ⓘ paramagnetism modeling ⓘ |
| usedIn |
Curie–Weiss law derivations
ⓘ
analysis of magnetocaloric effect ⓘ description of rare-earth paramagnets ⓘ design of paramagnetic thermometers ⓘ mean-field theory of ferromagnets ⓘ theory of localized magnetic moments ⓘ |
| usedToFit | experimental magnetization data ⓘ |
| variable | total angular momentum J = L + S ⓘ |
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: Brillouin function Description of subject: The Brillouin function is a mathematical function in statistical mechanics that describes the magnetization of a paramagnetic material as a function of temperature and applied magnetic field.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.