Accurate estimation of a phase diagram from a single STM image.

We propose a new approach to constructing a phase diagram using the effective Hamiltonian derived only from a single real-space image produced by scanning tunneling microscopy (STM). Currently, there have been two main methods to construct phase diagrams in material science: ab initio calculations and CALPHAD with thermodynamic information obtained by experiments and/or theoretical calculations. Although the two methods have successfully revealed a number of unsettled phase diagrams, their results sometimes contradicted when it is difficult to construct an appropriate Hamiltonian that captures the characteristics of materials, e.g., for a system consisting of multiple-scale objects whose interactions are essential to the system's characteristics. Meanwhile, the advantage of our approach over existing methods is that it can directly and uniquely determine the effective Hamiltonian without any thermodynamic information. The validity of our approach is demonstrated through an Mg-Zn-Y long-period stacking-ordered structure, which is a challenging system for existing methods, leading to contradictory results. Our result successfully reproduces the ordering tendency seen in STM images that previous theoretical study failed to reproduce and clarifies its previously unknown phase diagram. Thus, our approach can be used to clear up contradictions shown by existing methods.