  A number of problems arise when long-range forces, such as those governed by
Bessel functions, are used in particle-particle simulations. If a simple
cut-off for the interaction is used, the system may find an equilibrium
configuration at zero temperature that is not a regular lattice yet has an
energy lower than the theoretically predicted minimum for the physical system.
We demonstrate two methods to overcome these problems in Monte Carlo and
molecular dynamics simulations. The first uses a smoothed potential to truncate
the interaction in a single unit cell: this is appropriate for phenomenological
characterisations, but may be applied to any potential. The second is a new
method for summing the unmodified potential in an infinitely tiled periodic
system, which is in excess of 20,000 times faster than previous naive methods
which add periodic images in shells of increasing radius: this is suitable for
quantitative studies. Finally we show that numerical experiments which do not
handle the long-range force carefully may give misleading results: both of our
proposed methods overcome these problems.
