Triple

T17205091
Position Surface form Disambiguated ID Type / Status
Subject Kramers–Wannier duality in the Ising model E417578 entity
Predicate relatedTo P37 FINISHED
Object Onsager solution of the 2D Ising model
The Onsager solution of the 2D Ising model is the exact analytical solution, obtained by Lars Onsager in 1944, that determines the free energy and critical behavior of the two-dimensional Ising ferromagnet on a square lattice.
E1256774 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Onsager solution of the 2D Ising model | Statement: [Kramers–Wannier duality in the Ising model, relatedTo, Onsager solution of the 2D Ising model]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Onsager solution of the 2D Ising model
Context triple: [Kramers–Wannier duality in the Ising model, relatedTo, Onsager solution of the 2D Ising model]
  • A. Kramers–Wannier duality in the Ising model
    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.
  • B. Onsager reciprocal relations
    Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
  • C. Coleman theorem on symmetry breaking in two dimensions
    The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
  • D. Landau theory of second-order phase transitions
    Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Onsager solution of the 2D Ising model
Triple: [Kramers–Wannier duality in the Ising model, relatedTo, Onsager solution of the 2D Ising model]
Generated description
The Onsager solution of the 2D Ising model is the exact analytical solution, obtained by Lars Onsager in 1944, that determines the free energy and critical behavior of the two-dimensional Ising ferromagnet on a square lattice.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Onsager solution of the 2D Ising model
Target entity description: The Onsager solution of the 2D Ising model is the exact analytical solution, obtained by Lars Onsager in 1944, that determines the free energy and critical behavior of the two-dimensional Ising ferromagnet on a square lattice.
  • A. Kramers–Wannier duality in the Ising model
    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.
  • B. Onsager reciprocal relations
    Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
  • C. Coleman theorem on symmetry breaking in two dimensions
    The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
  • D. Landau theory of second-order phase transitions
    Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
  • E. 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.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d886d6ba8c819093215917b3d01689 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e42dc0bea8819090946615a14b2d86 completed April 19, 2026, 1:20 a.m.
NED1 Entity disambiguation (via context triple) batch_6a015fde8ba08190ae88dc9ea3366a68 completed May 11, 2026, 4:49 a.m.
NEDg Description generation batch_6a0161b31540819098aa6275f96433ad completed May 11, 2026, 4:57 a.m.
NED2 Entity disambiguation (via description) batch_6a016299d9ac8190be74d5db0d28ea36 completed May 11, 2026, 5:01 a.m.
Created at: April 10, 2026, 5:38 a.m.