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Topological expansion in the complex cubic log-gas model. One-cut case

Bleher, Pavel M., Deaño, Alfredo, Yattselev, Maxim (2016) Topological expansion in the complex cubic log-gas model. One-cut case. Journal of Statistical Physics, 166 (3-4). pp. 784-827. ISSN 0022-4715. E-ISSN 1572-9613. (doi:10.1007/s10955-016-1621-x)

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Abstract

We prove the topological expansion for the cubic log-gas partition function, with a complex parameter and defined on an unbounded contour on the complex plane. 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 Painleve I type. In the present paper we prove the topological expansion for the partition function 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.

Item Type: Article
DOI/Identification number: 10.1007/s10955-016-1621-x
Uncontrolled keywords: Log–gas model · Partition function · Topological expansion · Equilibrium measure · S-curve · Quadratic differential · Orthogonal polynomials · Non-Hermitian orthogonality · Riemann–Hilbert problem · Nonlinear steepest descent method
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Oct 2017 11:21 UTC
Last Modified: 05 Sep 2019 12:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/64099 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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