Langevin function
E829089
The Langevin function is a mathematical function that describes how the magnetization of a paramagnetic material depends on an applied magnetic field and temperature in classical statistical mechanics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Langevin function canonical | 3 |
| reduces to Langevin function for J → ∞ | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9921027 — 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: Langevin function Context triple: [Langevin theory of paramagnetism, defines, Langevin function]
-
A.
Brillouin function
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.
-
B.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
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C.
Onsager–Machlup function
The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Landau interaction function
The Landau interaction function is a central quantity in Fermi liquid theory that characterizes the effective quasiparticle–quasiparticle interactions near the Fermi surface.
- 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: Langevin function Target entity description: The Langevin function is a mathematical function that describes how the magnetization of a paramagnetic material depends on an applied magnetic field and temperature in classical statistical mechanics.
-
A.
Brillouin function
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.
-
B.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
-
C.
Onsager–Machlup function
The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Landau interaction function
The Landau interaction function is a central quantity in Fermi liquid theory that characterizes the effective quasiparticle–quasiparticle interactions near the Fermi surface.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical function
ⓘ
special function ⓘ |
| appearsIn |
Langevin model of paramagnetism
ⓘ
linked to:
Langevin theory of paramagnetism
classical theory of paramagnetism ⓘ |
| appliesTo |
classical paramagnetism
ⓘ
paramagnetic materials ⓘ |
| approximationOf | Brillouin function for large spin quantum number ⓘ |
| argumentRepresents |
ratio of magnetic energy to thermal energy
ⓘ
μ B / (k_B T) ⓘ |
| category |
functions in magnetism
ⓘ
functions in statistical mechanics ⓘ |
| definition | L(x) = coth(x) − 1/x ⓘ |
| derivedFrom |
Boltzmann statistics
ⓘ
linked to:
Boltzmann distribution
classical dipole moment distribution ⓘ |
| describes |
dependence of magnetization on applied magnetic field
ⓘ
dependence of magnetization on temperature ⓘ magnetization of a paramagnetic material ⓘ |
| domain | real numbers ⓘ |
| field |
classical physics
ⓘ
condensed matter physics ⓘ magnetism ⓘ statistical mechanics ⓘ |
| governs | classical paramagnetic magnetization curve saturation ⓘ |
| hasSeriesExpansion | L(x) = x/3 − x^3/45 + 2x^5/945 − … ⓘ |
| introducedIn | early 20th century ⓘ |
| inverseFunction | inverse Langevin function ⓘ |
| inverseUsedIn |
polymer chain elasticity models
ⓘ
rubber elasticity theory ⓘ |
| limitBehavior |
L(x) → 1 as x → ∞
ⓘ
L(x) → −1 as x → −∞ ⓘ L(x) ≈ x/3 for small x ⓘ |
| namedAfter | Paul Langevin ⓘ |
| property |
monotonic increasing function
ⓘ
odd function ⓘ |
| range | (−1, 1) ⓘ |
| relatedConcept |
Langevin equation
ⓘ
linked to:
Langevin dynamics
|
| relatedTo |
Brillouin function
ⓘ
Curie law ⓘ
linked to:
Curie law of magnetization
Curie–Weiss law ⓘ hyperbolic cotangent function ⓘ |
| symbol | L(x) ⓘ |
| usedFor |
determining magnetic moment from M–H data
ⓘ
magnetization curve fitting ⓘ |
| usedIn |
magnetic nanoparticle characterization
ⓘ
magnetic susceptibility calculations ⓘ superparamagnetism modeling ⓘ theory of paramagnetism ⓘ |
| variable | x ⓘ |
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: Langevin function Description of subject: The Langevin function is a mathematical function that describes how the magnetization of a paramagnetic material depends on an applied magnetic field and temperature in classical statistical mechanics.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Langevin function