Computer simulation of nanoscopic phase-inhomogeneous states and phase diagrams of HTSC cuprates and nickelates

More than 35 years of experience in the study of cuprate superconductors shows that the main characteristics of the phase diagram can only be obtained by taking into account mesoscopic static/dynamic phase inhomogeneity as a key property of these materials. Within a minimal model for the CuO$_2$/NiO$_2$ planes with the on-site Hilbert space reduced to only three effective valence centers [CuO$_4$]$^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory. Using Maxwell's construction, the global nature of the electronic phase separation in the CuO$_2$ planes of HTSC cuprates is established, which makes it possible to understand and explain many fundamental features of the physics of the normal and superconducting state of cuprates, including the mechanism of formation of the HTSC and pseudogap phase. The features of phase-inhomogeneous states and their evolution with temperature and doping degree, including the special role of the impurity potential in cuprates/nickelates with nonisovalent substitution, are considered for particular examples of the charge triplet model in the framework of the classical Monte Carlo method.