The partition function of the two-matrix model as an isomonodromic tau function

We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes that of Jimbo [ "Monodromy preserving deformation of linear ordinary differential equations with rational coefficients," Physica D 2, 306 (1981)]. In order to achieve the generalization we need to define a notion of tau function for isomonodromic systems where the adregularity of the leading coefficient is not a necessary requirement.