High Energy Physics - Phenomenology · arXiv:hep-ph/9709498 v4 · submitted 29 Sep 1997
"Lattice-Free" Simulations of Topological Defect Formation
The paper says
“This problem can be resolved by linearly interpolating the field values on the lattice, which gives results in good agreement with the continuum predictions.”
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The paper
Abstract
We examine simulations of the formation of domain walls, cosmic strings, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 component Gaussian random field, respectively. We derive analytic expressions for the corresponding topological defect densities in the continuum limit and show that they fail to agree with simulation results, even when the fields are smoothed on small scales to eliminate lattice effects. We demonstrate that this discrepancy, which is related to a classic geometric fallacy, is due to the anisotropy of the cubic lattice, which cannot be eliminated by smoothing. This problem can be resolved by linearly interpolating the field values on the lattice, which gives results in good agreement with the continuum predictions. We use this procedure to obtain a lattice-free estimate (for Gaussian smoothing) of the fraction of the total length of string in the form of infinite strings: f∞ = 0.716 ± 0.015.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.97
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.62 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.02 · states quantitative result 0.99 · compares with prior results 0.86 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v4). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We examine simulations of the formation of domain walls, cosmic strings, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 component Gaussian random field, respectively. | method 0.64 | 0.83 | 0.04 | asserted 0.93 |
| We derive analytic expressions for the corresponding topological defect densities in the continuum limit and show that they fail to agree with simulation results, even when the fields are smoothed on small scales to eliminate lattice effects. | result 0.96 | 0.95 | 0.20 | asserted 1.00 |
| We demonstrate that this discrepancy, which is related to a classic geometric fallacy, is due to the anisotropy of the cubic lattice, which cannot be eliminated by smoothing. | interpretation 0.92 | 0.87 | 0.32 | asserted 1.00 |
| This problem can be resolved by linearly interpolating the field values on the lattice, which gives results in good agreement with the continuum predictions. | method 0.82 | 0.91 | 0.37 | asserted 0.97 |
| We use this procedure to obtain a lattice-free estimate (for Gaussian smoothing) of the fraction of the total length of string in the form of infinite strings: $f_\infty = 0.716 \pm 0.015$. | result 1.00 | 0.96 | 0.31 | asserted 1.00 |
What kind of paper the classifier reports this is: method or tool 0.40 · evidence from simulation or computation 0.96
What was examined, and what was not
Sources read
- arXiv listing abstract v4
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- full text
- figures and tables
- references and citing sentences
- relations to other papers
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- P abstract
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- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,452 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 6 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Domain walls through different cosmologies astro-ph.CO · Jul 2026
- Abelian Higgs Cosmic Strings: Small Scale Structure and Loops hep-th · Dec 2008
- Extending and Calibrating the Velocity dependent One-Scale model for Cosmic Strings with One Thousand Field Theory Simulations astro-ph.CO · Nov 2019
- CMB power spectra from cosmic strings: predictions for the Planck satellite and beyond astro-ph.CO · May 2010
- Scaling in Numerical Simulations of Domain Walls hep-ph · Dec 2002
- The Cosmological Evolution of Domain Wall Networks hep-ph · Oct 2004
How the literature uses it
5 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 2 papers
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In the numerical implementation we calculate the (discretized) topological winding for monopoles given by the surface integral in Eq. [ref] as was done for 't Hooft-Polyakov monopoles [ref] .
Kibble mechanism for electroweak magnetic monopoles and magnetic fields · Kibble mechanism · 1.00
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Note that we also multiply by a factor of $π/6$ to account for the Manhattan effect [ref] .
Abelian-Higgs Cosmic String Evolution with CUDA · Discretization scheme · 0.93
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