Analysis Seminar

An application of integers of the 12th cyclotomic field in the theory of phase transitions

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 $d$.


Alik Mazel

Speaker Affiliation

AMC Health



Event Series


Date & Time
May 25, 2020 | 11:00am12:00pm


Remote Access via Zoom videoconferencing (link below)