Fig. 7.

Three-phase coexistence in Landau theory. (A) Phase diagram over membrane compositions ($\psi$) and tether compositions ($\rho$) calculated from Landau theory. Three phases coexist in the blue triangle, with the surface composition of each phase given by the vertices of the triangle. The positions within the triangle (black x) set the area fraction of phases. Three two-phase coexistence regions (red, purple, green) border the three-phase region and are plotted as tie lines. Surfaces constructed on a tie line split into two phases with compositions given by the ends of the tie line. Single-phase regions border each two-phase region. (B) Phase diagram over the surface chemical potentials ${\lambda }_{\rho },{\lambda }_{\psi }$ for the same system shown in A. The three-phase triangle is represented as the blue point, and each colored line corresponds to the two-phase regions in A. Outside of these lines and the point of three-phase coexistence the system is single phase. (C) Gradient construction within the three-phase region of A. The surface line is phase separated, folding in on itself and intersecting at the blue and yellow points. It additionally intersects with the bulk curve at high densities, green point.