ANNNI model

ANNNI model

The abbreviation ANNNI model stands for 'Axial Next-Nearest Neighbor Ising model'. It is a highly cited variant of one of the best known models in statistical physics, the Ising model. In that variant, competing ferromagnetic and
antiferromagnetic exchange interactions are coupling spins at nearest and next-nearest neighbor sites, along one of the crystallographic axes of the lattice. The model is describing in a prototypical fashion fascinating and complicated spatially modulated magnetic superstructures in
crystals.

The model was introduced in 1961 by (Sir) Roger Elliott from the University of Oxford, but only several years later, many of its intriguing properties had been analyzed and established (especially by Per Bak, Michael E. Fisher, Walter Selke, and Jacques Villain), providing a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures, aswell as accompanying phase transitions, in magnets, alloys, adsorbates, and other solids.

References

*cite journal
author = M.E. Fisher and W. Selke
date = 1980
title = Infininitely many commensurate phases in a simple Ising model
journal = Phys. Rev. Lett.
volume = 44
pages = 1502–1505
doi = 10.1103/PhysRevLett.44.1502

*cite journal
author = P. Bak
date = 1982
title = Commensurate phases, incommensurate phases, and the devil's staircase
journal = Reports on Progress in Physics
volume = 45
pages = 587–629
doi = 10.1088/0034-4885/45/6/001

*cite journal
author = W. Selke
date = 1988
title = The ANNNI model
journal = Physics Reports
volume = 170
pages = 213–264
doi = 10.1016/0370-1573(88)90140-8


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