From the point of view of thermodynamic, materials are found as thermodynamically stable (equilibrium) or metastable phases. These can be characterized via functions of state that depend uniquely on the given state variables such as temperature, pressure and composition. The graphical representations of all thermodynamically stable phases that exist or co-exist at equilibrium is called the phase diagram of the chemical system as function of the thermodynamic variables. The knowledge of equilibrium phases of chemical compounds as function of thermodynamic parameters and their thermodynamic stability lies at the foundation of our understanding of the properties and processes of modern materials. From the point of view of experimental methods, the determination of the thermodynamic functions and the equilibria between phases is an enormous task, especially at low temperature. For that reason it has become common practice to support the experimental research by a variety of theoretical calculations. Thus, in the seventies the project CALPHAD was started where different phenomenological models and general rules for the analysis and calculation of the phase diagrams were implemented. Over the past few years, calculations of phase diagrams and thermodynamic properties of materials have appeared in the literature, where typically information from experiment, such as the known existence of various ordered crystalline or solid solution-like phases, was combined with quantum mechanical computations. Clearly, such ab initio calculations can be very useful for the validation of existing phase diagrams. However, the reliance on experimental data is often a serious limitation, especially if one attempts to predict a phase diagram or is interested in competing metastable phases that might occur during the synthesis of new materials. Thus, it is necessary to develop a method to compute phase diagrams without experimental information. The general approach to the analysis of the low-temperature part of a (equilibrium) phase ...