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annni model wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 references toggle the table of contents annni model 4 languages deutsch italiano română 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia variant of the ising 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 the annni model 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 to describe experimental results on magnetic orderings in erbium the model was introduced in 1961 by roger elliott from the university of oxford 1 the model has given its name in 1980 by michael e fisher and walter selke 2 who analysed it first by monte carlo methods and then by low temperature series expansions showing the fascinating complexity of its phase diagram including devil s staircases and a lifshitz point indeed it provides for two and three dimensional systems a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures as well as accompanying phase transitions in various magnets alloys adsorbates polytypes multiferroics and other solids 3 4 further possible applications range from modeling of cerebral cortex to quantum information references edit 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 citeseerx 10 1 1 131 4735 doi 10 1088 0034 4885 45 6 001 cite journal cite uses deprecated parameter citeseerx help 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 retrieved from https en wikipedia org w index php title annni_model oldid 1182186960 categories statistical mechanics lattice models spin models hidden categories articles with short description short description matches wikidata cs1 errors deprecated parameters this page was last edited on 27 october 2023 at 17 52 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents annni model 4 languages add topic