  Finite size artifacts arise in molecular simulations of nucleation when
critical nuclei are too close to their periodic images. A rigorous
determination of what constitutes too close is, however, a major challenge.
Recently, we devised rigorous heuristics for detecting such artifacts based on
our investigation of how system size impacts the rate of heterogeneous ice
nucleation (Hussain, Haji-Akbari, \emph{J. Chem. Phys.} \textbf{154}, 014108,
\textbf{2021}). We identified the prevalence of critical nuclei spanning across
the periodic boundary, and the thermodynamic and structural properties of the
liquid occupying the inter-image region as indicators of finite size artifacts.
Here, we further probe the performance of such heuristics by examining the
dependence of homogeneous crystal nucleation rates in the Lennard-Jones liquid
on system size. The rates depend non-monotonically on system size and vary by
almost six orders of magnitude for the range of system sizes considered here.
We confirm that the prevalence of spanning critical nuclei is the primary
indicator of finite size artifacts and almost fully explains the observed
variations in rate. Proximity, or structuring of the inter-image liquid,
however, is not as strong of an indicator due to the fragmented nature of
crystalline nuclei. As a result, the dependence of rate on system size is
subtle for the systems with a minuscule fraction of spanning critical nuclei.
These observations indicate that our heuristics are universally applicable to
different modes of nucleation (homogeneous and heterogeneous) in different
systems even if they might be overly stringent for homogeneous
nucleation,~e.g.,~in the LJ system.
