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On the critical line the weights $a,b,c$ of the model are parameterized by a parameter $\\al>1$, as $a=\\frac{\\al-1}{2}$, $b=\\frac{\\al+1}{2}$, $c=1$. The asymptotics of $Z_N$ on the critical line was obtained earlier in the paper \\cite{BL2} of Bleher and Liechty: $Z_N=CF^{N^2}G^{\\sqrt{N}}N^{1/4}\\big(1+O(N^{-1/2})\\big)$, where $F$ and $G$ a"},"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":"1306.3510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"e5f77c5a3bb03d78ec78312eb357dcc8429aa266523c98f2588cfbd460e74479","abstract_canon_sha256":"f09076e17815c43c355cc29abfe8e9eca0631f48fab34447b48f7378eacb4053"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:05.792243Z","signature_b64":"1fp4psbaKRYrb81ReAsy/cxin24W0VuazEanMT5cPg5IR753R6hNqe24iMjCU+s72tkfd/+LLQYC/WMpExZKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","last_reissued_at":"2026-05-18T02:47:05.791728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:05.791728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calculation of the constant factor in the six-vertex model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Pavel Bleher, Thomas Bothner","submitted_at":"2013-06-14T20:39:37Z","abstract_excerpt":"In the present paper we calculate explicitly the constant factor $C$ in the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and ferroelectric phases. 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