ANNNI model

In statistical physics, the axial (or anisotropic) next-nearest-neighbor Ising model, usually known as the ANNNI model, is a variant of the Ising model in which competing ferromagnetic and antiferromagnetic exchange interactions couple spins at nearest and next-nearest neighbor sites along one of the crystallographic axes of the lattice. The model is a prototype for complicated spatially modulated magnetic superstructures in crystals.

The model was introduced in 1961 by Roger Elliott from the University of Oxford, but only given this name in 1980 by Michael E. Fisher and Walter Selke. It provides a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures, as well as accompanying phase transitions, in magnets, alloys, adsorbates, polytypes, multiferroics, and other solids.