Critical Behavior of Vortices in a Layered System

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Abstract
The critical behavior of vortices interacting in zero field in a system of weakly coupled layers is studied. A mathematically rigorous, real-space renormalization group study is carried out and the recursion relations derived. A new term is found which corresponds to the effect of vortex fluctuations on the interlayer coupling and which tends to decouple the layers just above the transition, a result which is consistent with Monte Carlo studies. The effect of vortices in neighboring layers on the critical behavior is also studied. We find that it reinforces slightly the upward shift of the transition temperature with the interlayer coupling, but is otherwise minimal over most of the temperature range.