  Isotropic pair potentials that are bounded at the origin have been proposed
from time to time as models of the effective interaction between macromolecules
of interest in the chemical physics of soft matter. We present a thorough study
of the phase behavior of point particles interacting through a potential which
combines a bounded short-range repulsion with a much weaker attraction at
moderate distances, both of Gaussian shape. Notwithstanding the fact that the
attraction acts as a small perturbation of the Gaussian-core model potential,
the phase diagram of the double-Gaussian model (DGM) is far richer, showing two
fluid phases and four distinct solid phases in the case that we have studied.
Using free-energy calculations, the various regions of confluence of three
distinct phases in the DGM system have all been characterized in detail.
Moreover, two distinct lines of reentrant melting are found, and for each of
them a rationale is provided in terms of the elastic properties of the solid
phases.
