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.
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