Is evaporation a kind of phase transition? When liquid is heat up to a critical temperature $T_{c}$, it starts boiling and converting to gas. In statistical mechanics, we learn that it is a phase transition. We studied all the properties near the critical temperature such as critical exponents.
However, evaporation can occur at all temperature, converting liquid phase to gas phase. So, I wonder if evaporation can be regarded as phase transition even though it seems to have no critical point.
Thanks.
 A: We should be a bit careful distinguishing the different scenarios.
The phase boundary one usually talks when we talk about the boiling of water is the point of equilibrium between (pure) liquid water and (pure) gaseous water. For this transition, there is a critical point at some $\left(P_c, T_c\right)$, connected to a line of first-order phase transitions $T_{boil}\left(P\right)$.
On the other hand, the situation with evaporation at room temperature is not the conversion between liquid water and gaseous water - indeed, from the phase diagram, we already know that the equilibrium state for pure water is a liquid at this temperature and pressure. If we had an enclosed box full of water and nothing else, with a piston so that it feels atmospheric pressure, it would be a liquid.
If I have a glass of water in my kitchen, however, it is not a system composed purely of water - now the system is composed of both water and air. Let's idealize the air as a single type of molecule, even though it has many. We now have three state variables - pressure, temperature, and water concentration. 
Since we have a two-component system, Gibbs' phase rule tells us that we can have two phases coexisting over a range of pressures and temperatures.
We can get some idea what these two phases are by considering a simple model of phase coexistence - e.g. something like two types of atoms moving around on a lattice, with some kind of interaction making atoms prefer to be next to atoms of the same type. The conclusion of this kind of analysis is that we can have coexistence between a phase which is mostly water with a small amount of dissolved air, and a phase which is mostly air with a small amount of dissolved water. (See e.g. Jones for this calculation.)
Thus, we conclude that the equilibrium state in my kitchen is a glass of water with a bit of air dissolved in it, and a room full of air with a bit of water dissolved in it. These two phases have the same free energy at this pressure and temperature, so they can coexist, and the relative amount of each is determined by conservation of mass (if I started out with more water in the room before equilibrating, I'll end up with a bigger water-rich phase.)
The usual evaporation scenario occurs because we are not in equilibrium, and the water concentration in the air is below its equilibrium value. So it is not a phase transition, so much as a system out of equilibrium moving toward equilibrium, as the comment by Samuel Weir pointed out. 
Incidentally, binary mixture models can also have phase transitions and a critical point. But I think this is not relevant here.
