Examples of renormalization group transformations for image sets

Journal Article · 26 November 2018 · Physical Review E

DOI: https://doi.org/10.1103/PhysRevE.98.052129 · OSTI ID:1504259

Foreman, Samuel ^[1]; Giedt, Joel ^[2]; Meurice, Yannick ^[3]; Unmuth-Yockey, Judah ^[4]

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1. Univ. of Iowa, Iowa City, IA (United States). Dept. of Physics and Astronomy; Argonne National Lab. (ANL), Argonne, IL (United States). Computational Sciences Division
2. Rensselaer Polytechnic Inst., Troy, NY (United States). Dept. of Physics, Applied Physics and Astronomy
3. Univ. of Iowa, Iowa City, IA (United States). Dept. of Physics and Astronomy
4. Syracuse Univ., NY (United States). Dept. of Physics

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occupation under the RG transformation, suggest ways to obtain data collapse, and compare with the two-state tensor RG approximation near the fixed point.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science - Graduate Student Research (SCGSR) Program; USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS) (SC-27)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1504259
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 98; ISSN PLEEE8; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English