Analysis Seminar

The construction of pure phases from ground states is performed for $ u > u_*(d)$ for all values of $d$ except for 39 special ones. For values $d$ with a single equivalence class all periodic ground states generate the corresponding pure phase which provides a complete description of extreme Gibbs measures (complete phase diagram). For a general $d$ we prove that at least one class of ground states generates pure phases and propose an algorithm that decides, after finitely many iterations, which classes of ground states generate pure phases. We cojecture that in case of several classes only one of them generates pure phases which is confirmed by (numerical) application of our algorithm to several (relatively small) values of $d$.