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, and other solids.

References

• R. J. Elliott (1961). "Phenomenological discussion of magnetic ordering in the heavy rare-earth metals". Phys. Rev. 124 (2): 346–353. Bibcode 1961PhRv..124..346E. doi:10.1103/PhysRev.124.346. 

• M.E. Fisher and W. Selke (1980). "Infinitely many commensurate phases in a simple Ising model". Phys. Rev. Lett. 44 (23): 1502–1505. Bibcode 1980PhRvL..44.1502F. doi:10.1103/PhysRevLett.44.1502. 

• P. Bak (1982). "Commensurate phases, incommensurate phases, and the devil's staircase". Reports on Progress in Physics 45 (6): 587–629. Bibcode 1982RPPh...45..587B. doi:10.1088/0034-4885/45/6/001. 

• W. Selke (1988). "The ANNNI model—Theoretical analysis and experimental application". Physics Reports 170 (4): 213–264. Bibcode 1988PhR...170..213S. doi:10.1016/0370-1573(88)90140-8.