Kramers–Wannier duality in the Ising model
E417578
concept in statistical mechanics
concept in theoretical physics
duality transformation
mathematical transformation
Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kramers–Wannier duality | 1 |
| Kramers–Wannier duality in the Ising model canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4142010 — 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: Kramers–Wannier duality in the Ising model Context triple: [Hendrik Anthony Kramers, knownFor, Kramers–Wannier duality in the Ising model]
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A.
Ising models
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.
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B.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
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C.
Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
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D.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
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E.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
- 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: Kramers–Wannier duality in the Ising model Target entity description: Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
-
A.
Ising models
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.
-
B.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
-
C.
Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
-
D.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
E.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
concept in theoretical physics ⓘ duality transformation ⓘ mathematical transformation ⓘ |
| appliesTo |
Ising models
ⓘ
surface form:
Ising model on the square lattice
two-dimensional Ising model ⓘ |
| assumes | infinite lattice limit for exact critical point determination ⓘ |
| category |
Ising models
ⓘ
surface form:
Ising model
critical phenomena ⓘ mathematical physics concepts ⓘ phase transitions ⓘ |
| concerns | partition function of the 2D Ising model ⓘ |
| demonstrates | equivalence of certain thermodynamic quantities at dual temperatures ⓘ |
| field |
lattice models of magnetism
ⓘ
statistical mechanics ⓘ |
| hasGeneralization |
duality in Z2 lattice gauge theory
ⓘ
duality transformations for Potts models ⓘ |
| historicalContext | introduced before Onsager’s exact solution of the 2D Ising model ⓘ |
| illustrates | symmetry between ordered and disordered phases ⓘ |
| implies |
critical point occurs where K equals K*
ⓘ
critical point of the square-lattice Ising model satisfies sinh(2Kc) = 1 ⓘ |
| inspired |
duality between spin models and gauge theories
ⓘ
modern notions of duality in quantum field theory ⓘ |
| involves |
Fourier-like transformation on spin configurations
ⓘ
re-expression of the partition function in terms of domain walls ⓘ |
| maps |
ordered phase to disordered phase
ⓘ
spin variables to dual spin or disorder variables ⓘ strong-coupling regime to weak-coupling regime ⓘ |
| namedAfter |
Gregory H. Wannier
ⓘ
Hendrik Anthony Kramers ⓘ |
| publishedIn | Physical Review ⓘ |
| relatedTo |
Onsager solution of the 2D Ising model
ⓘ
duality in lattice gauge theories ⓘ high–low temperature duality ⓘ order–disorder duality ⓘ |
| relates |
coupling constant K to dual coupling constant K*
ⓘ
high-temperature phase of the 2D Ising model ⓘ low-temperature phase of the 2D Ising model ⓘ partition function at temperature T to partition function at dual temperature T* ⓘ |
| reveals | location of the critical point of the 2D Ising model ⓘ |
| shows | self-duality of the 2D Ising model at its critical point ⓘ |
| usedFor | determining the critical temperature of the 2D Ising model ⓘ |
| usedIn |
pedagogical derivations of the Ising critical temperature
ⓘ
studies of universality and critical phenomena ⓘ |
| yearProposed | 1941 ⓘ |
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: Kramers–Wannier duality in the Ising model Description of subject: Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kramers–Wannier duality