Critical behavior of an array of Josephson junctions with variable couplings

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Abstract
We consider a generalization of the fully frustrated XY model in two dimensions, introduced by Berge et al. We derive the Coulomb gas representation of the partition function. From the form of the interaction between half-integer charges we infer that, away from full frustration, dipoles are formed out of neighboring charges and that the low-temperature phase transition is an Ising transition in this system of dipoles. The charges which are not bound in dipoles fuse in pairs to form a dilute gas of integer charges. The transition in this gas is a normal Kosterlitz-Thouless transition and is not triggered by the Ising transition. In fact, we make it plausible that the transitions only coincide at full frustration. Our picture is supported by Monte Carlo simulations.