Ordering of chirality for many planes of anyons

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Abstract
We consider the effect of interplane coupling on the energetics of the relative sign of statistics of anyons in adjacent planes. We offer qualitative arguments as well as numerical results which support the idea that opposing chirality (i.e., ‘‘antiferromagnetic’’ order of the statistics) is favored over a wide range of interplane coupling V–including both attractive and repulsive interactions between planes. We argue that our results apply to the normal (nonsuperfluid) phase in the thermodynamic limit.