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Exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic Wulff shape which is a regular hexagon: There are arbitrarily large $N$ with ground state configurations deviating from the nearest regular hexagon by a number of $\\sim N^{3/4}$ particles. We also prove that for any $N$ and any ground state configuration this deviation is bounded above by $\\sim N^{3/4}$. As a consequence we obtain an exact"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.6513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-26T17:47:17Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"365c9038c7fc71bbd670756d3332ff65a6b6300429fece0ef7844c70db17c8c6","abstract_canon_sha256":"13bc61c2d22cb92b687a8cac4377136e0ee5d6f3614d078181ba618b2f81b64c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:27.220748Z","signature_b64":"qnPcwotsSs66XAUBTZr8GA91mFSo5wZBsDlMCt5SMRM9G7n18tuJlPCARb727jxKuNU6m3alzt2g75Pq6U4aBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d2a1d1256636f6d5d96803c0d2e731b4e9e776b066e6d56683f3a0cf7645929","last_reissued_at":"2026-05-18T01:51:27.220185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:27.220185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states of the 2D sticky disc model: fine properties and $N^{3/4}$ law for the deviation from the asymptotic Wulff shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.AP","authors_text":"Bernd Schmidt","submitted_at":"2013-02-26T17:47:17Z","abstract_excerpt":"We investigate ground state configurations for a general finite number $N$ of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. 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