“…Taking the double scaling limit [9,10,11] to the critical point of this system, we succeeded in deriving the Painlevé II differential equation containing the parameter M ≡ α 1+2 + N = (m 2 − m 1 )/g s . See [12,8,5,1] and Appendix F of this paper for detail of these transcriptions or matrix model/4d gauge theory dictionary. This critical point is the simplest example of the Argyres-Douglas type points [13,14,15,1] well studied by using the Seiberg-Witten curve of cubic or quartic type [16,17].…”