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Eigenvalue-flipping Algorithm for Matrix Monte Carlo

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Samuel Kováčik, Juraj Tekel

High Energy Physics - Lattice · Submitted 10 Mar 2022

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

The authors' main claim In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally.

how it is stated · asserted 0.90 read the record →

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arXiv ID2203.05422 (version 2)
Pith IDGYW2QH3S, Pith's permanent record of this paper and its review
CitationJuraj Tekel, Samuel Kov\'a\v{c}ik. "Eigenvalue-flipping Algorithm for Matrix Monte Carlo." arXiv:2203.05422 (2022). https://pith.science/paper/GYW2QH3S
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,199 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.66 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.

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 Many physical systems can be described in terms of matrix models that we often cannot solve analytically. background 1.00 0.04 0.02 asserted 0.60
s1 Fortunately, they can be studied numerically in a straightforward way. background 1.00 0.05 0.02 asserted 0.98
s2 Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. background 0.58 0.07 0.04 asserted 1.00
s3 In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. contribution 0.96 0.86 0.77 asserted 0.90
s4 We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere. method 0.74 0.94 0.06 asserted 0.98

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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  • C citations
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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

Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.

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References
How the literature uses it

4 arXiv papers cite this in 9 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

Builds on it 1 paper
  • It was inspired by the eigenvalue-flipping algorithm of [ref] but is designed to work for models without the $Φ→-Φ$ symmetry, where flipping alone fails to connect inequivalent local minima.

    Eigenvalue-cluster Algorithm for Matrix Monte Carlo · Conclusion · 0.93

Uses its method or tool 2 papers
  • The numerical part consisted of the Hamiltonian Monte Carlo calculation of the full matrix integral, incorporating the eigenvalue-flipping algorithm [ref] and using two new order parameters ([ref], [ref]).

    Approximate treatment of noncommutative curvature in quartic matrix model · Conclusions and discussion · 1.00

  • We have used the HMC algorithm as described in [ref] with the eigenvalue procedure flipped off as it has not been tested in this context before.

    Fuzzy Onion as a Matrix Model · The $Φ^4$ scalar field theory · 0.99

What it cites · 15 sentences without a confident label

Compares with 1 paper
Cites as background 10 papers

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