Using operator covariance to disentangle scaling dimensions in lattice models Article Swipe
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2Δ}$ governed by scaling dimensions $Δ$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions can be extracted by data fitting, which is difficult when two or more powers contribute significantly. Here a method utilizing covariance between multiple lattice operators is developed where the $r$ dependent eigenvalues of the covariance matrix reflect scaling dimensions of individual field operators. This disentangling is demonstrated explicitly for conformal field theories. The scheme is first tested on the critical point of the 2D Ising model, where the two primary scaling dimensions and their respective two lowest descendant dimensions are extracted. The 3D Ising model is studied next, revealing the two relevant primaries and their lowest descendants to high precision. The 2D tricritical Ising point is studied with the Blume-Capel model. Here the scaling dimensions of all three symmetric primary operators are successfully isolated along with the leading descendants. The eigenvectors are also studied and give useful information on the boundary between the ordered and disordered phases in the neighborhood of the tricritical point. Finally, the crossover from regular to tricritical Ising scaling is investigated on several points on the phase boundary of the Blume-Capel model away from its tricritical point. The scaling of the eigenvalues corresponding to tricritical descendant operators are found to be remarkably stable even far from the tricritical point. The covariance method represents a simple extension of standard analysis of correlation functions and can significantly enhance the utility of Monte Carlo simulations and other computational methods in studies of criticality, in particular conformal critical points.
Related Topics
Concepts
Covariance
Scaling
Lattice (music)
Covariance mapping
Operator (biology)
Statistical physics
Mathematics
Covariance operator
Covariance function
Physics
Statistics
Covariance intersection
Geometry
Transcription factor
Gene
Biochemistry
Acoustics
Repressor
Chemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2406.12681
- https://arxiv.org/pdf/2406.12681
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399837732
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4399837732Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2406.12681Digital Object Identifier
- Title
-
Using operator covariance to disentangle scaling dimensions in lattice modelsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-06-18Full publication date if available
- Authors
-
Anders W. SandvikList of authors in order
- Landing page
-
https://arxiv.org/abs/2406.12681Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2406.12681Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2406.12681Direct OA link when available
- Concepts
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Covariance, Scaling, Lattice (music), Covariance mapping, Operator (biology), Statistical physics, Mathematics, Covariance operator, Covariance function, Physics, Statistics, Covariance intersection, Geometry, Transcription factor, Gene, Biochemistry, Acoustics, Repressor, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.correlation | 7, 245 |
| abstract_inverted_index.descendants | 127 |
| abstract_inverted_index.eigenvalues | 62, 216 |
| abstract_inverted_index.information | 168 |
| abstract_inverted_index.simulations | 256 |
| abstract_inverted_index.tricritical | 133, 183, 191, 210, 219, 232 |
| abstract_inverted_index.criticality, | 264 |
| abstract_inverted_index.demonstrated | 77 |
| abstract_inverted_index.descendants. | 159 |
| abstract_inverted_index.eigenvectors | 161 |
| abstract_inverted_index.investigated | 195 |
| abstract_inverted_index.neighborhood | 180 |
| abstract_inverted_index.simulations, | 27 |
| abstract_inverted_index.successfully | 153 |
| abstract_inverted_index.computational | 259 |
| abstract_inverted_index.corresponding | 217 |
| abstract_inverted_index.disentangling | 75 |
| abstract_inverted_index.significantly | 249 |
| abstract_inverted_index.significantly. | 46 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5033845918 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |