We propose an analytical thermodynamic model for describing defect phase transformations, which we term the statistical phase evaluation approach (SPEA). The SPEA model assumes a Boltzmann distribution of finite-size phase fractions and calculates their statistical average. To benchmark the performance of the model, we apply it to construct binary surface phase diagrams of metal alloys. Two.. Many industrial applications require a quick method to determine the chain length-dependent phase diagram of a given polymer solution, such as converting a solution polymerization into a precipitation polymerization, to greatly save the cost. However, it is rather difficult and time-consuming to precisely map phase diagrams of polymer solutions with different chain lengths, so that good phase.
One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a classification task. Typically, classification problems are tackled using discriminative classifiers that explicitly model the probability of the labels.. We investigate the quantum phases of the Hubbard model on this geometry using exact diagonalization, density matrix renormalization group, and perturbation theory. We construct a quantum phase diagram in the plane of the next-nearest-neighbor hopping parameter and onsite Coulomb interaction , revealing five distinct quantum phases.