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The model exhibits a super-rough glass phase at low temperature $T<T_{c}$ with relative displacements growing with distance $r$ as $\\bar{\\langle [\\theta(r)-\\theta(0)]^2\\rangle} \\simeq A(\\tau) \\ln^2 (r/a)$, where $A(\\tau) = 2 \\tau^2- 2 \\tau^3 +\\mathcal{O}(\\tau^4)$ near the transition and $\\tau=1-T/T_{c}$. We calculate all higher cumulants and show that they grow "},"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":"1304.4612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-16T20:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"0cfe6833806c385db243d8ac6cec5ac267f29026ff809e7666b8d4c1cdb22711","abstract_canon_sha256":"79a79b147b6ee1472c9ca163f51329cef5390f162bd1f5333454acf2ee8622c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:04.085325Z","signature_b64":"kSwD/cC4i3TCFWWTLCgYyRtrwEPXZ9yoAPjPkNqgpfh0pcZYHTgGPrZ689CzpiZm2zNc2Uh3OAR7H4kZPKX9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f23166fa0dd963e1c4f2a940b35dccf527a2a8bf4a6b0b52b8a2e99d59a29273","last_reissued_at":"2026-05-18T03:19:04.084603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:04.084603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact form of the exponential correlation function in the glassy super-rough phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay J\\\"org Wiese, Pierre Le Doussal, Zoran Ristivojevic","submitted_at":"2013-04-16T20:26:28Z","abstract_excerpt":"We consider the random-phase sine-Gordon model in two dimensions. It describes two-dimensional elastic systems with random periodic disorder, such as pinned flux-line arrays, random field XY models, and surfaces of disordered crystals. The model exhibits a super-rough glass phase at low temperature $T<T_{c}$ with relative displacements growing with distance $r$ as $\\bar{\\langle [\\theta(r)-\\theta(0)]^2\\rangle} \\simeq A(\\tau) \\ln^2 (r/a)$, where $A(\\tau) = 2 \\tau^2- 2 \\tau^3 +\\mathcal{O}(\\tau^4)$ near the transition and $\\tau=1-T/T_{c}$. 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