Triple

T23027987
Position Surface form Disambiguated ID Type / Status
Subject Coleman theorem on symmetry breaking in two dimensions E573375 entity
Predicate relatedTo P37 FINISHED
Object Mermin–Wagner theorem
The Mermin–Wagner theorem is a fundamental result in statistical physics and quantum field theory stating that continuous symmetries cannot be spontaneously broken at finite temperature in one- and two-dimensional systems with short-range interactions, thereby forbidding long-range order such as conventional ferromagnetism in these low dimensions.
E1565886 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: Mermin–Wagner theorem | Statement: [Coleman theorem on symmetry breaking in two dimensions, relatedTo, Mermin–Wagner theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mermin–Wagner theorem
Context triple: [Coleman theorem on symmetry breaking in two dimensions, relatedTo, Mermin–Wagner theorem]
  • A. Kosterlitz–Thouless–Halperin–Nelson–Young theory
    The Kosterlitz–Thouless–Halperin–Nelson–Young theory is a framework in condensed matter physics that explains phase transitions in two-dimensional systems via topological defects and the unbinding of vortex–antivortex pairs, rather than conventional symmetry breaking.
  • B. 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.
  • C. Landau–Peierls instability
    Landau–Peierls instability is a theoretical prediction in condensed matter physics that shows how long-wavelength thermal fluctuations destroy true long-range positional order in low-dimensional crystalline systems.
  • 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. 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.
  • 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: Mermin–Wagner theorem
Triple: [Coleman theorem on symmetry breaking in two dimensions, relatedTo, Mermin–Wagner theorem]
Generated description
The Mermin–Wagner theorem is a fundamental result in statistical physics and quantum field theory stating that continuous symmetries cannot be spontaneously broken at finite temperature in one- and two-dimensional systems with short-range interactions, thereby forbidding long-range order such as conventional ferromagnetism in these low dimensions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mermin–Wagner theorem
Target entity description: The Mermin–Wagner theorem is a fundamental result in statistical physics and quantum field theory stating that continuous symmetries cannot be spontaneously broken at finite temperature in one- and two-dimensional systems with short-range interactions, thereby forbidding long-range order such as conventional ferromagnetism in these low dimensions.
  • A. Kosterlitz–Thouless–Halperin–Nelson–Young theory
    The Kosterlitz–Thouless–Halperin–Nelson–Young theory is a framework in condensed matter physics that explains phase transitions in two-dimensional systems via topological defects and the unbinding of vortex–antivortex pairs, rather than conventional symmetry breaking.
  • B. 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.
  • C. Landau–Peierls instability
    Landau–Peierls instability is a theoretical prediction in condensed matter physics that shows how long-wavelength thermal fluctuations destroy true long-range positional order in low-dimensional crystalline systems.
  • 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. 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.
  • 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_69e245b821008190b0e09cb02092aae1 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f1847e48c48190894525c354663dd2 completed April 29, 2026, 4:09 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0bf2b3ac308190bc241acfd02903d8 completed May 19, 2026, 5:18 a.m.
NEDg Description generation batch_6a0bf70818608190b6d7c5ee633bb4ce completed May 19, 2026, 5:37 a.m.
NED2 Entity disambiguation (via description) batch_6a0bf76284988190ac4b8f08859aecc6 completed May 19, 2026, 5:38 a.m.
Created at: April 17, 2026, 3:52 p.m.