According to Gibbs, an ideal thermodynamic system would have finitely many phases (e.g., solid, liquid, gas) that would be separated by a (branched) smooth manifold; the "phase transition locus".

In the context of the thermodynamic formalism, we show that this ideal picture holds at temperature zero for subshifts of finite type and locally constant potentials, i.e., for one-dimensional Ising models. The phase transtition locus has a natural structure of a tropical hypersurface. O-minimality plays an important role.