Phase Diagram of the Square-Lattice ANNNI Model

The phase diagram of the square-lattice ANNNI (axial next nearest-neighbor Ising) model in an external field is calculated by the interface method of Mullerhartmann and Zittartz. In the ANNNI model, next nearest-neighbor interactions are assumed to be antiferromagnetic whereas others take both ferromagnetic and antiferromagnetic values. The stability of various commensurate phases predicted for the ground state are examined against the formation of an interface separating two different regions, each consisting of one of the degenerate ground states. The phase diagrams display different commensurate phases having no common boundary between them so that the critical temperature is zero on the multiphase boundaries. For a certain set of parameters, the phase diagram is favorably compared with the Monte Carlo result obtained by Rujan and co-workers.