Low-temperature phase diagram of the ANNNI model in a magnetic field

Abstract

The phase diagram of the (d>2)-dimensional axial next-nearest-neighbour Ising (ANNNI) model in a non-zero magnetic field is considered in the context of the low-temperature series expansion technique of Fisher and Selke (1980, 81). It is argued that, with careful use of this technique, all of the infinitely many commensurate phases which spring from the multiphase point in zero field must also persist in sufficiently small non-zero fields. This result, which is verified explicitly in the leading orders of the expansion, corrects a recent calculation of Smith and Yeomans (1982) which suggested the complete absence of half of the phases in any non-zero field.