Branching processes in the ANNNI model

Abstract

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-13), 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^l3)^m(2^l+13)ⁿ) or ((23^l)^m(23^l+1)ⁿ), where l, m and n are integers.