To appear in Journal of Statistical Physics Colligative properties of solutions: II. Vanishing concentrations

We continue our study of colligative properties of solutions initiated in ref. [1]. We focus on the situations where, in a system of linear size L, the concentration and the chemical potential scale like c = ξ/L and h = b/L, respectively. We find that there exists a critical value ξt such that no phase separation occurs for ξ ≤ ξt while, for ξ> ξt, 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