Approximations to the configurational energy of dipolar particles on a 2D lattice

Abstract

Current research on critical phenomena and minimum energy configurations of dipolar particles on a 2D lattice, usually approximates the infinite interaction range through a cutoff to carry out numerical simulations. In this work we compare the commonly reported procedure in, literature, consisting of truncating the potential function from a given abscissa, to another proposed method, where the function is vertically shifted to zero after the truncation. We show that the first procedure renders more mistakes than the second, where mistakes still admittedly occur but their appearance notably decreases as a function of distance. We also examined the conditions necessary to consider discrete dipoles as being continuous beyond the cutoff position and found that the shifted procedure performs better than truncating alone.