{"paper":{"title":"Exact ground states of one-dimensional long-range random-field Ising magnets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.comp-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Alexander K. Hartmann, Timo Dewenter","submitted_at":"2013-07-15T15:21:06Z","abstract_excerpt":"We investigate the one-dimensional long-range random-field Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability $p \\sim r^{-1-\\sigma}$, where $r$ is the distance between these spins and $\\sigma$ is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to $L = 2^{19}$ via graph theoretical algorithms for four different values of $\\sigma \\in \\{0.25,0.4,0.5,1.0\\}$ while varying the strength $h$ of the random fields. For each "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3987","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":""},"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"}