Unsupervised machine learning approach for detecting second order phase transition in three-dimensional liquid mixtures

Phase transition is one of the most challenging topic in physical chemistry because of not only its unusual singularity at the phase transition point, but also the drastic change of thermodynamic properties that makes mathematical description difficult. In this study we deal with the specific part of the phase transition, which is called phase separation or mixing-demixing transition. This can usually be observed when the temperature or density of the mixture changes. In order to capture the phase separation point, it is necessary to run simulations based on grand canonical ensemble or Gibbs ensemble, but these ensembles are in general not applicable to the simulations with complex molecules. Therefore, we introduce unsupervised machine learning to detect the phase separation in symmetric binary mixtures and this technique can be applied for usual canonical or isothermal-isobaric ensemble simulations. We find that by using Principal Component Analysis(PCA) on two model systems, Lennard-Jones(LJ) binary mixture and Widom-Rowlinson mixture, we can observe the drastic change of order parameter and diverging heat capacity on the critical temperature, which shows the clear evidences of critical behavior. We also find that the change of PCA-derived order parameter from LJ binary mixture shows the critical exponent $\beta$ which is included in 3D Ising universality class, and the standard deviation of PCA clusters behaves like heat capacity and its critical exponent is also close to its universality class. Additionally, we compare two different types of feature vector in order to see the importance of constructing appropriate feature vectors for the system. We find that the feature vector based on the Euclidean distance is not an appropriate choice for the system with high dimension. Moreover, the feature vector based on the concentration fluctuation works more accurately whatever the type of mixtures or the space dimensions are.