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We consider the two-dimensional uniformly frustrated XY model in the limit ofsmall frustration, which is equivalent to an XY system, for instance aJosephson junction array, in a weak uniform magnetic field applied along adirection orthogonal to the lattice. We show that the uniform frustration(equivalently, the magnetic field) destabilizes the line of fixed points whichcharacterize the critical behaviour of the XY model for T <= T_{KT}, whereT_{KT} is the Kosterlitz-Thouless transition temperature: the system isparamagnetic at any temperature for sufficiently small frustration. We predictthe critical behaviour of the correlation length and of gauge-invariantmagnetic susceptibilities as the frustration goes to zero. These predictionsare fully confirmed by the numerical simulations.

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