  We show that classical many-particle systems interacting with certain soft
pair interactions in two dimensions exhibit novel low-temperature behaviors.
Ground states span from disordered to crystalline. At some densities, a large
fraction of normal-mode frequencies vanish. Lattice ground-state configurations
have more vanishing frequencies than disordered ground states at the same
density and exhibit vanishing shear moduli. For the melting transition from a
crystal, the thermal expansion coefficient is negative. These unusual results
are attributed to the topography of the energy landscape.
