{"paper":{"title":"Loop erased random walk on percolation cluster: Crossover from Euclidean to fractal geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"E. Daryaei, S. Rouhani","submitted_at":"2013-08-26T20:14:17Z","abstract_excerpt":"We study loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\\geq p_c$, in two and three dimensions. We find that the fractal dimensions of LERW$_p$ is close to normal LERW in Euclidean lattice, for all $p>p_c$. However our results reveal that LERW on critical incipient percolation clusters is fractal with $d_{f}=1.217\\pm0.0015$ for d = 2 and $1.44\\pm0.03$ for d = 3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5692","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}