Exact ground state energy of a system with an arbitrary number of dipoles at the sites of a regular one-dimensional crystal lattice

Abstract

We consider a finite classical system of electric dipoles localized at the sites of a regular one-dimensional crystal lattice. It is shown that the ground state energy of such a system can be calculated exactly for an arbitrary number of dipoles. The expression for the ground state energy can be given in terms of special functions such as Riemann zeta functions and polygamma functions for any arbitrary number of dipoles, and reduces to the correct result in the thermodynamic limit as the number of dipoles tends to infinity. Simpler, but very accurate, approximate expressions for the ground state energy are also introduced.