Competing Interactions and Patterns in Nanoworld by Elena Vedmedenko

By Elena Vedmedenko

Platforms exhibiting competing interactions of a few sort are common - even more, in reality, as typically expected (magnetic and Ising-type interactions or the dynamics of DNA molecules being merely well known examples).Written for researchers within the box with diverse expert backgrounds, this quantity classifies phenomena no longer by way of process yet particularly through the kind of competing interactions concerned. this permits for an easy presentation of the underlying ideas and the common legislation governing the behaviour of alternative systems.Starting with a ancient evaluate, the writer proceeds via describing self-competitions of assorted sorts of interactions (such as diploar or multipolar interactions), competitions among a short-range and a long-range interplay (as in Ising structures or DNA versions) or among a long-range interplay and an anisotropy (as in ultrathin magnetic motion pictures or magnetic nanoparticles) and at last competitions among interactions of an identical variety (as in spin glasses).Each bankruptcy features a few issues of options which offer compatible fabric for teachers of arithmetic and physics in addition to biology courses.A significant physique of references to the unique literature make the quantity self-contained and best to grasp this interdisciplinary box.

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Example text

In quasicrystals, the situation is different since, as the pattern consists of two tiles with edges of equal length, this distance is usually taken as the nearest-neighbor distance. The shorter diagonal bonds are, usually, neglected in the calculations [26]. Such disregard is physically questionable as the exchange coupling increases exponentially with decreasing interatomic distance. In the following section the short diagonal of the rhombus and the sides of the motifs (see Fig. 7) will be considered as nearest neighbors.

11 d). For a non-collinear alignment of neighboring magnetic moments hEi should be non-integral, as the cosines of the angles between the moments are no longer zero or unity. This occurs for all other tilings considered here (compare Fig. 11 a–c). The average energy of non-collinear XY configurations is almost equal to that of a collinear Ising solution. In the case of the Heisenberg model, the minimal possible local energy peak increases from –8 J to approximately –6 J for JH ˆ J (see Fig. 7).

3 (a) One possible Ising antiferromagnetic ground state on a triangular lattice with low statistical weight. (b) Low-temperature Monte-Carlo configuration of an Ising antiferromagnet with high statistical weight on a triangular lattice. The different colors represent different orientations of spins. 1 Number of ground state configurations W for triangular-shaped samples on a triangular lattice of N sites. 5 Self-Competition of the Short-Range Interactions figurations increases drastically with the size of a lattice.

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