Successful theory of anharmonicity in the classical limit

We present a critical assessment of the equation-of-state results for a fac e-centered-cubic Lennard-Jones solid calculated from two entirely different summation procedures for an infinite set of free-energy diagrams. The firs t 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 Have ordering scheme, but arising in d ifferent orders of perturbation theory (PT), are summed to infinity. The se cond procedure is the self-consistent phonon theory (SC) which has been in use for some time. Tn the first-order version of this theory (SC1), only th e first order PT diagrams are summed and in the improved self-consistent (I SC) theory the first important contribution (cubic term) arising from the s econd-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 theo ry by averaging the cubic tensor force constant and also without averaging this constant (ISCU). This brings out the effect of averaging which is a ne cessary requirement in the SCI 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 ag reement with MC results. [S0163-1829(99)13741-X].