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We assume that the potential $V$ admits the representation \\[V(\\eta):=-\\log\\int\\varrho({d}\\kappa)\\exp\\biggl[-{1/2}\\kappa\\et a^2\\biggr],\\] where $\\varrho$ is a positive measure with compact support in $(0,\\infty)$. Hence, the potential $V$ is symmetric, but nonconvex in general. While for strictly convex $V$'s, the translation-invariant, ergodic gradient Gibbs measures are completely characterized by their t"},"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":"0704.3086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-04-23T20:45:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b9e331b80404636c0a31138cda75bf80bf0634f836b25078537f51b7f77b12dd","abstract_canon_sha256":"b8d53a122cb42fd7c4fc0c5f85bbe34b480c04baf7651dfce5105014272c4b5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:00.887016Z","signature_b64":"MRqb43wlKVLiCUl0eKi8mlIyUR0fo9dWKRv5IVHWvuOCWAS5fdN7GDusdQCFnA+1u4igsoYv24kKZFG689cwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab173077a5b8f4b00318270602bd3bd76ffa882307b98683f4436b88368075b1","last_reissued_at":"2026-05-18T04:34:00.886358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:00.886358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling limit for a class of gradient fields with nonconvex potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Herbert Spohn, Marek Biskup","submitted_at":"2007-04-23T20:45:20Z","abstract_excerpt":"We consider gradient fields $(\\phi_x:x\\in \\mathbb{Z}^d)$ whose law takes the Gibbs--Boltzmann form $Z^{-1}\\exp\\{-\\sum_{< x,y>}V(\\phi_y-\\phi_x)\\}$, where the sum runs over nearest neighbors. We assume that the potential $V$ admits the representation \\[V(\\eta):=-\\log\\int\\varrho({d}\\kappa)\\exp\\biggl[-{1/2}\\kappa\\et a^2\\biggr],\\] where $\\varrho$ is a positive measure with compact support in $(0,\\infty)$. Hence, the potential $V$ is symmetric, but nonconvex in general. 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