The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behavior of the XY model for T ≤ TKT, where TKT is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behavior of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations. © 2008 IOP Publishing Ltd.