{"paper":{"title":"Topological Expansion in the Complex Cubic Log-Gas Model. One-Cut Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Alfredo Dea\\~no, Maxim Yattselev, Pavel M. Bleher","submitted_at":"2016-06-14T10:55:35Z","abstract_excerpt":"We prove the topological expansion for the cubic log-gas partition function \\[ Z_N(t)= \\int_\\Gamma\\cdots\\int_\\Gamma\\prod_{1\\leq j<k\\leq N}(z_j-z_k)^2 \\prod_{k=1}^Ne^{-N\\left(-\\frac{z^3}{3}+tz\\right)}\\mathrm dz_1\\cdots \\mathrm dz_N, \\] where $t$ is a complex parameter and $\\Gamma$ is an unbounded contour on the complex plane extending from $e^{\\pi \\mathrm i}\\infty$ to $e^{\\pi \\mathrm i/3}\\infty$. The complex cubic log-gas model exhibits two phase regions on the complex $t$-plane, with one cut and two cuts, separated by analytic critical arcs of the two types of phase transition: split of a cut "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04303","kind":"arxiv","version":1},"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"}