Results for the ground state energy of a finite system of dipoles in a one-dimensional crystal lattice

We investigate the ground state energy of a finite classical system consisting of an arbitrary number of electric dipoles localized at the sites of a regular one-dimensional crystal lattice. The ground state energy per dipole can be exactly calculated in the thermodynamic limit but an exact analytical expression for the energy valid for an arbitrary finite number of dipoles is not possible. In this work we obtain an approximate analytical expression for the ground state energy that applies to any given finite number of dipoles. The approximate analytical expression that we report reproduces the exact numerically calculated values of the ground state energy with an astonishing accuracy