Exactly solvable model for cantorus phase transitions

A new class of exactly solvable Frenkel-Kontorova models is studied. For any fixed irrational winding number w, we find examples of nonrecurrent minimum-energy configurations, the existence of which has hitherto been in doubt. Such incommensurate defects nucleate a «devil's-staircase» type of ground-state phase transitions, corresponding to discontinuous transformations of cantori in the associated area-preserving maps. These minimizing cantori may have several independent orbits of gaps and are accompanied by an infinity of metastable cantori with the same w