Phase diagram of 3D ANNNI model in an effective-field approximation

TL;DR

This paper develops an effective-field method to analyze the phase diagram of the 3D ANNNI model, revealing complex phase structures and transition behaviors consistent with previous studies.

Contribution

It introduces a new effective-field approach for 3D lattice spin models and applies it to the ANNNI model to map its detailed phase diagram.

Findings

Confirmed the complex phase diagram with multiple commensurate and incommensurate phases.

Localized transition lines for various commensurate structures.

Provided evidence against direct transitions between commensurate and disordered phases.

Abstract

An effective-field method for caculation of thermodynamic properties of three-dimensional lattice spin models is developed. It is applied to the ANNNI model on the simple cubic lattice. The phase diagram of the model, consisting of a large number of commensurate phases and of an incommensurate phase, is calculated, confirming the results of previous approaches. The phase transition lines for a number of commensurate structures are localized, and a strong evidence for absence of the direct phase transition between commensurate phases and the disordered phase is found.