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Finding hidden order in spin models with persistent homology

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Bart Olsthoorn, Johan Hellsvik, Alexander V. Balatsky

Statistical Mechanics · Submitted 10 Sep 2020

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

The authors' main claim In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids.

how it is stated · asserted 1.00 read the record →

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arXiv ID2009.05141 (version 1)
Pith IDCEHJOE3D, Pith's permanent record of this paper and its review
CitationAlexander V. Balatsky, Bart Olsthoorn, Johan Hellsvik. "Finding hidden order in spin models with persistent homology." arXiv:2009.05141 (2020). https://pith.science/paper/CEHJOE3D
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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, 3,532 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids. By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram.

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 Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. background 1.00 0.03 0.02 asserted 1.00
s1 In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids. contribution 0.96 0.92 0.88 asserted 1.00
s2 By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. method 0.97 0.90 0.06 asserted 1.00
s3 Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram. method 0.87 0.85 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from simulation or computation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids. By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram.

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References
How the literature uses it

5 arXiv papers cite this in 6 sentences

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 citing it · 5 sentences without a confident label

Cites it as background 1 paper

What it cites · 2 sentences without a confident label

Cites as background 1 paper

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