Correlated Einstein model for the equilibrium properties of solids

The correlated Einstein model (CEM) is a new approach to the problem of determining the equilibrium properties of anharmonic solids. It is based on the use of the zeroth-order term in an expansion for the average of a product of one- and two-particle functions, where the average is a classical canonical average for a system of independent Einstein oscillators. The parameters that characterize the oscillators are chosen so that the first- and second-order terms in the expansion vanish. A diagrammatic representation of the expansion is given. Explicit formulas for determining the Helmholtz free energy of a monatomic cubic crystal are given and are evaluated both for a Lennard-Jones and a $\frac{1}{r^{12}}$ potential. The results obtained are compared with available Monte Carlo values. The CEM is found to be at least as accurate as the uncorrelated-pairs approximation, the cell-cluster method, the simple cell model, and improved self-consistent phonon theory.