Line Phase Transitions

Phenomena of adsorption in nonstandard geometries and, in particular, wetting on curved surfaces display new and unexpected features. Contrary to recent expectations adsorption phase transitions on cylindrical substrates can continue to exist when the bulk correlation length $\xi$ of the adsorbate becomes much larger than the cylinder radius $r_1$. The global phase diagram for wetting on cylinders features two regimes, "surface" transitions ($\xi \lesssim r_1<\infty$) and "line" transitions ($0<\mathrm{}{r}_1\lesssim \xi$), which become connected at a critical double point. For spherical substrates, the global wetting phase diagram is qualitatively the same as for cylinders.