Recent Progress in Using the Effective Potential Method

Abstract

The effective potential method has been developed over the last eight years, starting from an original simple approximation of Feynman’s [1]. A substantially better approximation was introduced by Riccardo Giachetti and Valerio Tognetti [2, 3] and by Feynman and Kleinert [4]. In both original and the improved methods, the partition function is obtained in a classical form but with an effective potential. The application to fairly realistic systems has been made by Tognetti and his co-workers, including Alessandro Cuccoli and Ruggero Vaia [7], and by our group at Rutgers, which has included Shudun Liu, Zizhong Zhu, Dominic Acocella, and Eugene Freidkin. We have shown that the use of this effective potential in a classical Monte Carlo calculation (EPMC) yields thermodynamic properties for the heavier inert-gas solids which agree closely at high temperatures with classical Monte Carlo results, at low temperatures with anharmonic perturbation theory, and succeed in interpolating smoothly between the two [8, 9, 10]. Here we shall first review the general idea of the method, and then we discuss two recent applications which test the applicability of the method further. Finally we shall speculate a little about the future prospects of the method.