Anomalous melting and solid polymorphism of a modified inverse-power potential

We numerically investigate a system of particles interacting through a repulsive pair potential of inverse-power form, modified in such a way that the strength of the repulsion is softened in a range of distances. The solid phases of the system for various levels of softness are identified by computing the zero-temperature phase diagram; then, for each solid phase, the melting line is determined by Monte Carlo simulation. Upon increasing the softness of the potential core, a region appears where melting occurs upon compression at constant temperature ('anomalous' melting) and a number of low-coordinated crystals become stable at moderate pressures. Next, the structural properties of the system for varying core softness are surveyed in the hypernettedchain approximation, whose accuracy has been positively tested against numerical simulation. For sufficiently high degrees of softness, the radial distribution function shows the typical interplay between two distinct lengthscales. In a narrow range of moderate softness, reentrant melting occurs instead with just one length-scale, which shows that the existence of two well-definite length-scales is not the only mechanism for anomalous melting.