{"paper":{"title":"Renormalization group for Anderson localization on high-dimensional lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Antonello Scardicchio, Boris L. Altshuler, Carlo Vanoni, Piotr Sierant, Vladimir E. Kravtsov","submitted_at":"2024-03-04T12:16:35Z","abstract_excerpt":"We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $\\beta$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson transition on random regular graphs. We show how in the delocalized region, including the transition point, the one-parameter scaling part of the $\\beta$-function for the fractal dimension $D_{1}$ evolves smoothly from its $d=2$ form, in which $\\beta_2\\leq 0$, to its $\\beta_\\infty\\geq 0$ form, which is represented by the regular random graph (RRG) result. We show how"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.01974","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.01974/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}