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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, 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, as
well as accompanying phase transitions, in magnets, alloys, and other solids.

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References

References

★ Infininitely many commensurate phases in a simple Ising model, M.E. Fisher and W. Selke, , , Phys. Rev. Lett.,

★ Commensurate phases, incommensurate phases, and the devil's staircase, P. Bak, , , Reports on Progress in Physics,

★ The ANNNI model, W. Selke, , , Physics Reports,