In theormodynamics phase transitions can for example be classified by the behavior of the order parameter (Landau) or by the continuity of thermodynamic functions and their derivatives (Ehrenfest).

How can the different kinds of phase transitions classified by the above methods (such as first order, second order, continuous, $\lambda$ point) be described from a RG flow point of view? What exactly does the RG flow field in the corresponding parameter space look like near a first order, second order, etc phase transition?