For first order metal-insulator transitions we show that, together with the dc conductance zero, there is a second critical point where the dielectric constant becomes zero and further turns negative. At this point the metallic reflectivity sharply increases. The two points can be separated by a phase separation state in a 3D disordered system but may tend to merge in 2D. For illustration we evaluate the dielectric function in a simple effective medium approximation and show that at the second point it turns negative. We reproduce the experimental data on a typical Mott insulator such as MnO, demonstrating the presence of the two points clearly. We discuss other experiments for studies of the phase separation state and a similar phase separation in superconductors with insulating inclusions. DOI: 10.1103/PhysRevLett.101.226407 PACS numbers: 71.30.+h, 71.55.Jv, 74.25.Dw, 78.67.Àn The charge transport and metal-insulator transitions (MITs) in disordered systems have been discussed in many papers [1][2][3], reviews [4,5], and books [6][7][8][9]. The initial discussion resulted in agreement that at T ¼ 0 the transition is completely described by the dc conduction as a function of the Fermi level at T ¼ 0. This is true for second order MITs, where simultaneously with the vanishing of the conductance the real part of the dielectric function also vanishes. It is negative in the metallic state and positive in the dielectric one, and there is no phase separation in this case. Here we show that in a first order MIT in composites the dc conduction is not enough and the dc dielectric constant has to be considered in order to make the description complete. We will show that in a first order MIT in the composites, in disordered thermodynamically metastable 3D systems, there can be an intermediate two phase region separating the metallic state from the dielectric one, both at T ¼ 0 and at finite temperatures. We will consider such a metal-dielectric composite with a metallic volume fraction f, but our results are relevant for other first order MITs in homogeneous systems, due to the nucleation of metallic inclusions in the dielectric matrix under pressure, for example. In a composite, grains of both components are always present for any metallic volume fraction f Þ 0 and f Þ 1, and the resistance drop occurs at a volume fraction f c different from the dielectric function sign change f d and in different samples made with different metallic volume fractions. Under pressure due to different compressibility, a composite irreversibly can undergo both transitions. To illustrate this, we show a noncomposite example of the phase separation in the Mott insulator . It demonstrates both the resistance drop near 90 GPa and the subsequent reflectance sharp increase, which becomes pressure-independent at 127 GPa [13]. The data from Ref. [12] are given in Fig. 1, and a detailed discussion of MITs in MnO is given in [14].Specific phase separation state.-A metallic 3D sample is screening any static electric fields as well as the electrone...