  Hybrid particle-field molecular dynamics is a molecular simulation strategy
wherein particles couple to a density field instead of through ordinary pair
potentials. Traditionally considered a mean-field theory, a momentum and
energy-conserving hybrid particle-field formalism has recently been introduced,
which was demonstrated to approach the Gaussian Core model potential in the
grid-converged limit. Here, we expand on and generalize the correspondence
between the Hamiltonian hybrid particle-field method and particle-particle pair
potentials. Using the spectral procedure suggested by Bore and Cascella, we
establish compatibility to any local soft pair potential in the limit of
infinitesimal grid spacing. Furthermore, we document how the mean-field regime
often observed in hybrid particle-field simulations is due to the systems under
consideration, and not an inherent property of the model. Considering the
Gaussian filter form in particular, we demonstrate the ability of the
Hamiltonian hybrid particle-field model of recovering all structural and
dynamical properties of the Gaussian Core model, including solid phases, a
first-order phase transition, and anomalous transport properties. We quantify
the impact of the grid spacing on the correspondence, as well as the effect of
the particle-field filtering length scale on the emergent particle-particle
correlations.
