{"paper":{"title":"Interacting partially directed self avoiding walk. From phase transition to the geometry of the collapsed phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G.B. Nguyen, N. P\\'etr\\'elis, P. Carmona","submitted_at":"2013-06-20T14:27:08Z","abstract_excerpt":"In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by $\\beta$ and $f$, respectively. The IPDSAW is known to undergo a collapse transition at $\\beta_c$. We provide the precise asymptotic of the free energy close to criticality, that is we show that $f(\\beta_c-\\epsilon)\\sim \\gamma \\epsilon^{3/2}$ where $\\gamma$ is computed explicitly and interpreted in terms of an associated continuous model. We also establish so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4887","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"}