ANNNI model

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The abbreviation ANNNI-Modell stands for axially next-nearest neighbor Ising model . It is a variant of the Ising model known in statistical mechanics .

In the ANNNI model it is assumed that in addition to the ferromagnetic Ising coupling between neighboring spins along a selected axis of a crystal lattice between the next but one spins there is a competing , i.e. antiferromagnetic, interaction. This leads to frustration . In particular, the model describes complex, spatially modulated, magnetic superstructures commensurate or incommensurable with the crystal lattice structure, as well as phase transitions between such structures.

The properties of the model are not only of theoretical interest, but also allow the interpretation of numerous experiments, among others. a. to phase diagrams of magnets , alloys and adsorbates . The ANNNI model has been used as a starting point for descriptions in very different areas, ranging from structures of the cortex to quantum information and the study of quantum phase transitions.

The model was first mentioned in the physical literature in 1961 in a paper by Roger James Elliott , University of Oxford . A first detailed analysis of the phase diagram was carried out by Michael E. Fisher and Walter Selke , who also gave the model its current name. Other important analyzes can be achieved a. Per Bak and Jacques Villain .

literature

Individual evidence

  1. ^ Gordon L. Shaw, Dennis J. Silverman, and John C. Pearson: Model of Cortical Organization Embodying a Basis for a Theory of Information Processing and Memory Recall . In: PNAS . tape 82 , no. 8 , 1985, pp. 2364-2368 , JSTOR : 25099 .
  2. Amit Dutta, Gabriel Aeppli, Bikas, K. Chakrabarti, Uma Divakaran, Thomas F. Rosenbaum and Diptiman Sen: Quantum phase transitions in transverse field spin models: From Statistical Physics to Quantum Information (2015) .