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. Statistical physics is one of the fundamental theories of Physics, and uses methods of Statistics in solving physical problems The Ising model, named after the physicist Ernst Ising, is a mathematical model in Statistical mechanics. 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. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules usuallyrelated to the spins of Electrons align in a regular pattern with neighboring In Physics, the exchange interaction is a Quantum mechanical effect which increases or decreases the expectation value of the Energy or Distance In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Geometry and Crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation The model is describing in a prototypical fashion fascinating and complicated spatially modulated magnetic superstructures in crystals. A superstructure is an upward extension of an existing structure above a baseline In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating
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, adsorbates, and other solids. Knight is the English term for a social position originating in the Middle Ages. The University of Oxford (informally "Oxford University" or simply "Oxford" located in the city of Oxford, Oxfordshire, England is the Per Bak ( December 8 1948 - October 16 2002) was a Danish theoretical physicist, attributed with the development of Michael Ellis Fisher (born 3 September 1931 in Trinidad) is a physicist as well as chemist and mathematician known for his many seminal contributionsto Walter Selke (born 1947) is a German professor for Theoretical Physics at the RWTH Aachen. In Mathematics, two non- Zero Real numbers a and b are said to be commensurable Iff a / b In Mathematics, two non- Zero Real numbers a and b are said to be commensurable Iff a / b In Thermodynamics, phase transition or phase change is the transformation of a thermodynamic system from one phase to another A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. An alloy is a Solid solution or Homogeneous mixture of two or more elements, at least one of which is a Metal, which itself has In Chemistry and Surface science, an adsorbate is a substance adhered to a surface (the adsorbent A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume.
References
- M.E. Fisher and W. Selke (1980). Michael Ellis Fisher (born 3 September 1931 in Trinidad) is a physicist as well as chemist and mathematician known for his many seminal contributionsto Walter Selke (born 1947) is a German professor for Theoretical Physics at the RWTH Aachen. "Infininitely many commensurate phases in a simple Ising model". Phys. Rev. Lett. 44: 1502–1505. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
- P. Bak (1982). Per Bak ( December 8 1948 - October 16 2002) was a Danish theoretical physicist, attributed with the development of "Commensurate phases, incommensurate phases, and the devil's staircase". In Mathematics, a singular function is any function &fnof( x) defined on the interval ''b'' that has the following properties Reports on Progress in Physics 45: 587–629. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
- W. Selke (1988). Walter Selke (born 1947) is a German professor for Theoretical Physics at the RWTH Aachen. "The ANNNI model". Physics Reports 170: 213–264. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
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