  We study a very simple model of a short-range attraction and an outer shell
repulsion as a test system for demixing phase transition and density anomaly.
The phase-diagram is obtained by applying mean field analysis and Monte Carlo
simulations to a two dimensional lattice gas with nearest-neighbors attraction
and next-nearest-neighbors repulsion (the outer shell). Two liquid phases and
density anomaly are found.
  The coexistence line between these two liquid phases meets a critical line
between the fluid and the low density liquid at a tricritical point. The line
of maximum density emerges in the vicinity of the tricritical point, close to
the demixing transition.
