Solitons and phasons in the Ising model with competing interactions

Abstract

We report an analysis of the spatially modulated phase of an Ising model with competing interactions. The mean-field phase diagram, as calculated numerically, includes a large, possibly infinite, number of transitions between commensurate phases. The main features can be understood in terms of a domain wall, or "soliton" picture. Near the transitions, the solitons form a regular lattice. The elementary excitations in this lattice are the phasons. The effects of fluctuations which have been ignored in the mean field theory can be estimated by calculating the phason entropy. Only two commensurate phases, with periodicities 4 and 6 lattice units, respectively, survive at finite temperature. The remaining part of the phase diagram is a floating incommensurate phase.