Non-monotonic behavior of the Binder Parameter in the discrete spin systems

We study a non-monotonic behavior of the Binder parameter, which appears in the discrete spin systems. Using the Fortuin-Kasteleyn graph representation, we find that the improved estimator of the Binder parameter consists of two terms with values only in high- and low-temperature regions. The non-monotonic behavior is found to originate from the low-temperature term. With the appropriately defined order parameter, we can reduce the influence of the low-temperature term, and as a result, the non-monotonic behavior can also be reduced. We propose new definitions of the order parameter, which reduces or eliminates the non-monotonic behavior of the Binder parameter in a system for which the improved estimator of the Binder parameter is unknown.Comment: 23 pages, 12 figures, added new result

Configuration sampling in multi-component multi-sublattice systems enabled by ab Initio Configuration Sampling Toolkit (abICS)

Simulation of the intermediate levels of disorder found in multi-component multi-sublattice systems in various functional materials is a challenging issue, even for state-of-the-art methodologies based on first-principles calculation. Here, we introduce our open-source package ab Initio Configuration Sampling Toolkit (abICS), which combines high-throughput first-principles calculations, machine learning, and parallel extended ensemble sampling in an active learning setting to enable such simulations. The theoretical background is reviewed in some detail followed by brief notes on usage of the software. In addition, our recent applications of abICS to multi-component ionic systems and their interfaces for energy applications are reviewed as demonstration of the power of this approach.Comment: 25 pages, 6 figure

Data-analysis software framework 2DMAT and its application to experimental measurements for two-dimensional material structures

An open-source data-analysis framework 2DMAT has been developed for experimental measurements of two-dimensional material structures. 2DMAT| offers five analysis methods: (i) Nelder-Mead optimization, (ii) grid search, (iii) Bayesian optimization, (iv) replica exchange Monte Carlo method, and (v) population-annealing Monte Carlo method. Methods (ii) through (v) are implemented by parallel computation, which is efficient not only for personal computers but also for supercomputers. The current version of 2DMAT is applicable to total-reflection high-energy positron diffraction (TRHEPD), surface X-ray diffraction (SXRD), and low-energy electron diffraction (LEED) experiments by installing corresponding forward problem solvers that generate diffraction intensity data from a given dataset of the atomic positions. The analysis methods are general and can be applied also to other experiments and phenomena.Comment: 11 pages, 8 figure