Álvarez Galindo, GabrielMartínez Alonso, LuisMedina Reus, Elena2023-06-182023-06-182015-08-150377-042710.1016/j.cam.2014.11.054https://hdl.handle.net/20.500.14352/24025© Elsevier Science Bv. We thank Prof. A. Martínez Finkelshtein for useful conversations and for calling our attention to the work [20]. The financial support of the Ministerio de Ciencia e Innovación under project FIS2011-22566 is gratefully acknowledged.We apply the method we have described in a previous paper (2013) to determine the phase structure of asymptotic zero densities of the standard cubic model of non-Hermitian orthogonal polynomials. We provide a complete description of the two phases: the one cut phase and the two cut phase, and analyze the phase transition processes of the types: splitting of a cut, birth and death of a cut. (C) 2014 Elsevier B.V. All rights reserved.engjournal articlehttp://dx.doi.org/10.1016/j.cam.2014.11.054http://www.sciencedirect.comopen access51-73Riemann-hilbert approachValued weight functionMatrix modelsExponential weightsRespectUniversalityFísica-Modelos matemáticosFísica matemática