Quantifying resolution in cosmological N-body simulations using
  self-similarity
  We demonstrate that testing for self-similarity in scale-free simulations
provides an excellent tool to quantify the resolution at small scales of
cosmological N-body simulations. Analysing two-point correlation functions
measured in simulations using ABACUS, we show how observed deviations from
self-similarity reveal the range of time and distance scales in which
convergence is obtained. While the well-converged scales show accuracy below 1
percent, our results show that, with a small force softening length, the
spatial resolution is essentially determined by the mass resolution. At later
times the lower cut-off scale on convergence evolves in comoving units as
$a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it
is set by two-body collisionality. A corollary of our results is that N-body
simulations, particularly at high red-shift, contain a significant spatial
range in which clustering appears converged with respect to the time-stepping
and force softening but has not actually converged to the physical continuum
result. The method developed can be applied to determine the resolution of any
clustering statistic and extended to infer resolution limits for non-scale-free
simulations.
