Abstract:
Double scaling limit of hermitian matrix model $\Phi^6$ to the first Painlevé equation ($\mathbb{P}_1$) and the next higher equation in $\mathbb{P}_1$ hierarchy ($\mathbb{P}_1^2$) is studied. In the first case is proved to obtain the desired limit the contour of integration must be modified. In the second case is shown that the limit exists without any modification.