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Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating the energy of all structures using ordinary quantum ab initio methods can be significantly time-consuming. Machine learning can be a reliable alternative to ab initio methods. We calculate the energy of these compounds with an accuracy close to that of density functional theory calculations in a considerably shorter time using machine learning. In this study, we use kernel ridge regression and neural network to predict energy. In the KRR, we employ sine matrix, Ewald sum matrix, SOAP, ACSF, and MBTR. To implement the neural network, we use two important classes of application of the neural network in material science, including high-dimensional neural network and convolutional neural network based on crystal graph representation. We show that kernel ridge regression using MBTR and neural network using ACSF can provide better accuracy than other methods. [Display omitted] [ABSTRACT FROM AUTHOR]

We present ESpinS (Esfahan Spin Simulation) package to evaluate the thermodynamic properties of spin systems described by a spin model Hamiltonian. In addition to the Heisenberg exchange term, the spin Hamiltonian in ESpinS can contain interactions such as bi-quadratic, Dzyaloshinskii–Moriya, and single-ion anisotropy. By applying the classical Monte Carlo simulation, ESpinS simulates the behavior of spin systems with respect to temperature. ESpinS can calculate the specific heat, susceptibility, staggered magnetization, energy histogram, fourth-order Binder cumulants, and neutron scattering structure factor. Further, it can compute the user-defined magnetic order parameter, that is, the summation of the projection of spins on the user-defined directions and the physical quantities based on it. ESpinS works with both a local update algorithm and a parallel tempering algorithm. The latter is an appropriate option for considering frustrated and spin-glass magnetic systems. ESpinS is written in Fortran 90 and can be run in single or parallel mode. The package is freely available under the GPL license (https://github.com/nafiserb/ESpinS). [Display omitted] [ABSTRACT FROM AUTHOR]