{"paper":{"title":"The Little-Hopfield model on a Random Graph","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"I. P\\'erez Castillo, N.S. Skantzos","submitted_at":"2003-09-29T08:51:14Z","abstract_excerpt":"We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0309655","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"}