  We continue our study of colligative properties of solutions initiated in
math-ph/0407034. We focus on the situations where, in a system of linear size
$L$, the concentration and the chemical potential scale like $c=\xi/L$ and
$h=b/L$, respectively. We find that there exists a critical value $\xit$ such
that no phase separation occurs for $\xi\le\xit$ while, for $\xi>\xit$, the two
phases of the solvent coexist for an interval of values of $b$. Moreover, phase
separation begins abruptly in the sense that a macroscopic fraction of the
system suddenly freezes (or melts) forming a crystal (or droplet) of the
complementary phase when $b$ reaches a critical value. For certain values of
system parameters, under ``frozen'' boundary conditions, phase separation also
ends abruptly in the sense that the equilibrium droplet grows continuously with
increasing $b$ and then suddenly jumps in size to subsume the entire system.
Our findings indicate that the onset of freezing-point depression is in fact a
surface phenomenon.
