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,[1] but only given this name in 1980 by Michael E. Fisher and Walter Selke.[2] It provides a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures,[3] as well as accompanying phase transitions, in magnets, alloys, adsorbates, polytypes, multiferroics, and other solids. Further applications range from modeling of cortex to quantum information.[4]