Special Microscopic-States-Basis Representation of Macroscopic Structure for Discrete Thermodynamic Systems

For a classical discrete system under constant composition, the macroscopic structure in a thermodynamically equilibrium state can be typically determined through the so-called canonical average, including the sum over possible configurations on a configuration space. Although a set of configurations predominantly contributing to equilibrium properties should depend on temperature and many-body interactions, we have recently clarified that at a high temperature, they are well characterized by a single special configuration (which we call projection state: PS), whose structure can be known a priori without any thermodynamic information. Here, we extend this approach to finding additional special configurations, enabling us to characterize equilibrium structures for a low-temperature region above the transition temperature. We demonstrate the validity of the proposed additional configurations by comparing temperature dependence of short-range ordering tendency from the conventional thermodynamic simulation.