Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook.

If the volume tends to infinity, some complex roots of the macro partition function may converge to some points $z_0,z_1,z_2,\dots$ on the real axis. Thus these $\{ z_n \}$ divide the complex plane to some isolated phases. According to the singularity near the $\{z_n\}$ every two neighboring phases may have phase transition phenomena occurr.

Here comes my question. Considering three phases surrounding a triple point in a phase diagram, they can transit to each other (just think about water). *Since neighborhood along the real axis consists of only two possibilities, I wonder if this theory could account for a description of the triple point.* And what is the connection between neighborhood of patches on the complex plane and the neighborhood of phases in a phase diagram?

This post imported from StackExchange Physics at 2014-08-11 14:59 (UCT), posted by SE-user huotuichang