Perturbation theory for very long-range potentials

Abstract

Systems with very long-range interactions (that decay at large distances like U(r)∼r−l with l≤d where d is the space dimensionality) are difficult to study by conventional statistical mechanics. Examples of these systems are gravitational and charged (non-electroneutral). In this work we propose two alternative methodologies to avoid these difficulties and capture some of the properties of the original potential. The first one consists of expressing the original potential in terms of a finite sum of hard-core Yukawa potentials. In the second one, the potential is rewritten as a damped potential, using a damping function with a parameter that controls the range of the interaction. These new potentials with finite ranges, which mimic the original one, can now be treated by conventional statistical mechanics methods.