Successful theory of anharmonicity in the classical limit

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Abstract
We present a critical assessment of the equation-of-state results for a face-centered-cubic Lennard-Jones solid calculated from two entirely different summation procedures for an infinite set of free-energy diagrams. The first is the recent procedure given by Shukla and Cowley [R.C. Shukla and E.R. Cowley, Phys. Rev. B 58, 2596 (1998)], where the diagrams of the same order of magnitude generated from the Van Hove ordering scheme, but arising in different orders of perturbation theory (PT), are summed to infinity. The second procedure is the self-consistent phonon theory (SC) which has been in use for some time. In the first-order version of this theory (SC1), only the first order PT diagrams are summed and in the improved self-consistent (ISC) theory the first important contribution (cubic term) arising from the second-order PT, omitted in SC1, is included as a correction to the SC1 free energy. We have calculated the equation-of-state results from the ISC theory by averaging the cubic tensor force constant and also without averaging this constant (ISCU). This brings out the effect of averaging which is a necessary requirement in the SC1 theory but not in ISC. The results from the SC1 and ISCU are poor. The results from the ISC and Shukla-Cowley summation procedures agree with each other at low temperature. At high temperatures, the ISC results are in poor agreement with the classical Monte Carlo (MC) results, whereas the Shukla-Cowley procedure yields results in excellent agreement with MC results.