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Non-integrable dimer models: universality and scaling relations

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Alessandro Giuliani (Roma Tre), Fabio Lucio Toninelli (Universite de Lyon, CNRS)

Probability · Submitted 10 May 2019

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

The authors' main claim It turns out that GFF behavior is connected with a remarkable identity (`Haldane' or 'Kadanoff relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations.

how it is stated · asserted 1.00 read the record →

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arXiv ID1905.04011 (version 1)
Pith IDYCCOWXW2, Pith's permanent record of this paper and its review
CitationAlessandro Giuliani (Roma Tre), CNRS), Fabio Lucio Toninelli (Universite de Lyon. "Non-integrable dimer models: universality and scaling relations." arXiv:1905.04011 (2019). https://pith.science/paper/YCCOWXW2
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The compiled record

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, 3,758 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctuations. It turns out that GFF behavior is connected with a remarkable identity (`Haldane' or 'Kadanoff relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations.

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 In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. background 1.00 0.07 0.07 asserted 1.00
s1 In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. contribution 0.89 0.44 0.07 asserted 0.57
s2 In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctuations. contribution 0.85 0.26 0.13 asserted 0.65
s3 It turns out that GFF behavior is connected with a remarkable identity (`Haldane' or 'Kadanoff relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations. result 0.74 0.33 0.44 asserted 1.00

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.64.

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not examined
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  • P abstract
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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

In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctuations. It turns out that GFF behavior is connected with a remarkable identity (`Haldane' or 'Kadanoff relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • In this paper, we prove the identity between the critical exponent of the two-point dimer correlation and the amplitude of this massless Gaussian field.

    Haldane relation for interacting dimers · 0.85

What it cites · 19 sentences without a confident label

Uses the method or tool of 1 paper
  • For instance, with $g(·)$ as in [ref], [equation] In Fourier space (with the conventions of [ref] for the Grassmann fields in momentum space) one has [equation] where [equation] Similar formulas hold for $r=2,3,4$, with $W_1(k,p)$ replaced by $W_r(k,p)$.

    Non-integrable dimers: Universal fluctuations of tilted height profiles · First-order computation of $A$ · 0.81

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