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A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

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Jerome Benoit, Rossen Dandoloff

Mathematical Physics · Submitted 24 Apr 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice.

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arXiv IDmath-ph/0004029 (version 2)
Pith ID4AUOETMU, Pith's permanent record of this paper and its review
CitationJerome Benoit, Rossen Dandoloff. "A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices." arXiv:math-ph/0004029 (2000). https://pith.science/paper/4AUOETMU
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,176 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.79 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. result 0.94 0.94 0.67 asserted 1.00
s1 For the antiferromagnetic chain we recover the Haldane decomposition. result 0.99 0.83 0.07 asserted 1.00
s2 This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. interpretation 0.49 0.79 0.21 asserted 0.98
s3 In fact this merely corresponds to a novel extension of the spin group by a local gauge field. interpretation 0.98 0.75 0.17 asserted 0.97
s4 This analysis based on the real division algebras applies to low dimensional lattices. limitation 0.52 0.63 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.

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