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By Elena Vedmedenko

Platforms showing competing interactions of a few style are common - even more, in truth, as in most cases expected (magnetic and Ising-type interactions or the dynamics of DNA molecules being simply renowned examples).Written for researchers within the box with diverse specialist backgrounds, this quantity classifies phenomena now not by means of process yet relatively by way of the kind of competing interactions concerned. this enables for an easy presentation of the underlying ideas and the common legislation governing the behaviour of other systems.Starting with a old evaluation, the writer proceeds through describing self-competitions of varied 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 analogous diversity (as in spin glasses).Each bankruptcy features a few issues of suggestions which supply appropriate fabric for academics of arithmetic and physics in addition to biology courses.A massive physique of references to the unique literature make the amount self-contained and superb to grasp this interdisciplinary box.

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Lett. 2000, 85, 302. I. M. Kuli, H. Schiessel, Phys. Rev. Lett. 2003, 91, 148103. S. L. Shumway, J. P. Sethna, Phys. Rev. Lett. 1991, 67, 995. B. Hu, B. Li, Europhys. Lett. 1999, 46, 655. N. J. Zabusky, M. D. Kruskal, Phys. Rev. Lett. 1965, 15, 240. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Wiley-VCH, Weinheim, 1982. I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik, B. G. Teubner Verlagsgesellschaft, Stuttgart and Nauka, Moskau, 1991. W. F. Brown, Magnetostatic principles in ferromagnetism.

1. On a triangular lattice the four sites involved form a minimal diamond (see Fig. 15). As Eq. 15) comprises scalar products of neighboring spins, it should be frustrated on a triangular lattice by analogy with the antiferromagnetic Heisenberg model. The resulting magnetic structure, however, should be different from that of the Néel ordering because of the hopping term. Fig. 15 Example of minimal diamond clusters on a triangular lattice. 43 44 2 Self-Competition: or How to Choose the Best from the Worst Fig.

Such a cooperative phenomenon is denoted as “spin-liquid” behavior [46]. The spin-liquid phases result from an energy landscape that has a continuum of energetically equivalent states, with low or nonexistent barriers between them. Experimentally, the spin-liquid phase is often found in so-called pyrochlores – compounds having a three-dimensional lattice structure formed by the coresharing tetrahedra. One example is polycrystalline Tb2Ti2O7, a pyrochlore antiferromagnet in which rare-earth Tb3+ ions have strong magnetic moments.

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