Branching processes in the ANNNI model

The mean-field equations of the simple cubic ANNNI model are studied on finite lattices. The results are consistent with the sequence of distinct commensurate phases (2 k-1 3), k=1,2,3,..., springing from the multiphase point, found using low-temperature series expansions. Moreover, evidence for new structure combination branching processes is presented, which generate phases of type ((2 l 3) m (2 l+1 3) n ) or ((23 l ) m (23 l+1 ) n ), where l, m and n are integers.