Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry

Details Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry

2010-06-23

arxiv.org/abs/1006.4515v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 7 figures, contribution to ICQ11 (Sapporo, Japan 2010) conference proceedings

Scientific paper

In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a structure having pentagonal loops. Such five-fold loops can be expected to occur naturally in quasicrystals, as seen for example in a number of experimental studies of surfaces of icosahedral alloys. Our model considers classical vector spins placed on vertices of a subtiling of the two dimensional Penrose tiling, and interacting with nearest neighbors via antiferromagnetic bonds. We give a set of recursion relations for this system, which consists of an infinite set of embedded clusters with sizes that increase as a power of the golden mean. The magnetic ground states of this fractal system are studied analytically, and by Monte Carlo simulation.

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