On the configuration of systems of interacting particle with minimum potential energy per particle

In continuation of previous work we extend the class of two-body potentials, either repulsive or of generalized Lennard-Jones type, for which it can be proved that among all configurations of an infinite one-dimensional system of interacting particles (with fixed density in the case of repulsive interaction) the configuration where all particles are equidistant has the minimum potential energy per particle. It is shown that this property does not hold for the repulsive potential φ(x) = (1 + x4)−1.