Josephson-junction arrays in transverse magnetic fields: Ground states and critical currents

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Abstract
Josephson-junction arrays in transverse magnetic fields are most simply described by uniformly frustrated XY models. Frustration in these models is parametrized by f, the ratio of the magnetic flux through one cell of the array to the magnetic flux quantum. We propose a quasi-one-dimensional structure for the ground states of these models, valid for (1/3)≤f≤(1/2). The energies and zero-temperature critical currents for this structure can be calculated exactly. For rational f=p/q, energies and critical currents are functions of q only; for irrational f, they are independent of f. Numerical calculations of the ground-state form agree with this quasi-one-dimensional conjecture for several f in the range (1/3)≤f≤(1/2). .AE