{"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. While for strictly convex $V$'s, the translation-invariant, ergodic gradient Gibbs measures are completely characterized by their t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3086","kind":"arxiv","version":3},"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"}