Unusual phase behavior of one-component systems with two-scale isotropic interactions

We study the phase behavior of systems of particles interacting through pair potentials with a hard core plus a soft repulsive component. We consider several different forms of soft repulsion, including a square shoulder, a linear ramp and a quasi-exponential tail. The common feature of these potentials is the presence of two repulsive length scales, which may be the origin of unusual phase behaviors such as polyamorphism both in the equilibrium liquid phase and in the glassy state, water-like anomalies in the liquid state and anomalous melting at very high pressures.