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In the context of magnetism, frustration arises when a group of spins cannotfind a configuration that minimizes all of their pairwise interactionssimultaneously. We consider the effects of the geometric frustration thatarises in a structure having pentagonal loops. Such five-fold loops can beexpected to occur naturally in quasicrystals, as seen for example in a numberof experimental studies of surfaces of icosahedral alloys. Our model considersclassical vector spins placed on vertices of a subtiling of the two dimensionalPenrose tiling, and interacting with nearest neighbors via antiferromagneticbonds. We give a set of recursion relations for this system, which consists ofan infinite set of embedded clusters with sizes that increase as a power of thegolden mean. The magnetic ground states of this fractal system are studiedanalytically, and by Monte Carlo simulation.

Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry