Inclusion of higher order anharmonic contributions in self-consistent phonon theory

The ansatz method of infinite summation of higher order diagrams given in S hukla and Cowley, Phys. Rev. B 58, 2596 (1998), is extended to the self-con sistent phonon theory. We demonstrate the high accuracy of this approach wi th respect to the first-order self-consistent and improved self-consistent (ISC) phonon theories, by comparing the results from the ansatz method with their exact counterparts. The ISC theory is then extended to include the r emaining diagrams of O(lambda(4)), which could not be included in its earli er formulation. This makes the ISC theory consistent, at least to O(lambda( 4)). This ISC theory offers a substantial improvement over the current ISC theory. The results of the equation of state for a face centered cubic near est neighbor interaction Lennard-Jones solid from our ISC theory are shown to be in excellent agreement with the results of the classical Monte Carlo method also obtained for the same model.