Bleher, PavelDeaño, AlfredoYattselev, Maxim2017-05-042017-05-042017-02Bleher, P., Deaño, A., & Yattselev, M. (2017). Topological Expansion in the Complex Cubic Log–Gas Model: One-Cut Case. Journal of Statistical Physics, 166(3–4), 784–827. https://doi.org/10.1007/s10955-016-1621-xhttps://hdl.handle.net/1805/12470We prove the topological expansion for the cubic log–gas partition function ZN(t)=∫Γ⋯∫Γ ∏1≤j<k≤N (zj−zk)2 N ∏ k=1 e−N(− z3 3 +tz)dz1⋯dzN, where t is a complex parameter and Γ is an unbounded contour on the complex plane extending from eπi∞ to eπi/3∞. 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 and birth of a cut. The common point of the critical arcs is a tricritical point of the Painlevé I type. In the present paper we prove the topological expansion for logZN(t) in the one-cut phase region. The proof is based on the Riemann–Hilbert approach to semiclassical asymptotic expansions for the associated orthogonal polynomials and the theory of S-curves and quadratic differentials.enPublisher Policylog-gas modelpartition functiontopological expansionArticle