  The relation between liquid-liquid phase transitions and waterlike density
anomalies in core-softened potentials of fluids was investigated in an exactly
solvable one dimensional lattice model and a in a three dimensional fluid with
fermi-like potential, the latter by molecular dynamics. Both systems were shown
to present three liquid phases, two liquid-liquid phase transitions closely
connected to two distinct regions of anomalous density increase. We propose
that an oscillatory behavior observed on the thermal expansion coefficient as a
function of pressure can be used as a signature of the connection between
liquid-liquid phase and density.
