{"paper":{"title":"Reversible boolean networks II: Phase transition, oscillation, and local structures","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.DS","nlin.AO","nlin.CG","physics.comp-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Leo P. Kadanoff, S. N. Coppersmith, Zhitong Zhang","submitted_at":"2000-09-01T21:17:10Z","abstract_excerpt":"We continue our consideration of a class of models describing the reversible dynamics of $N$ Boolean variables, each with $K$ inputs. We investigate in detail the behavior of the Hamming distance as well as of the distribution of orbit lengths as $N$ and $K$ are varied. We present numerical evidence for a phase transition in the behavior of the Hamming distance at a critical value $K_c\\approx 1.65$ and also an analytic theory that yields the exact bounds on $1.5 \\le K_c \\le 2.$\n  We also discuss the large oscillations that we observe in the Hamming distance for $K<K_c$ as a function of time as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0009019","kind":"arxiv","version":2},"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"}