{"paper":{"title":"The Binomial Spin Glass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","physics.comp-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Gerardo Ortiz, Martin Weigel, Mohammad-Sadegh Vaezi, Zohar Nussinov","submitted_at":"2017-12-22T18:21:10Z","abstract_excerpt":"To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the {\\it binomial} spin glass, a class of models where the couplings are sums of $m$ identically distributed Bernoulli random variables. In the continuum limit $m \\to \\infty$, the class reduces to one with Gaussian couplings, while $m=1$ corresponds to the $\\pm J$ spin glass. We demonstrate that for short-range Ising models on $d$-dimensional hypercubic lattices the ground-state entropy density for $N$ spins is bounded from above by $(\\sqrt{d/2m} + 1/N)\\ln2$, and further show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08602","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"}