A class of uniformly frustrated xy models which describe the behavior of a Josephson-junction array in a transverse magnetic field is considered. The frustration f is the fraction of flux quantum of applied field per unit cell of the lattice. The ground-state energy E₀ and critical current are computed for several rational f. The behavior for arbitrary f is discussed, and it is concluded that the resistive transition temperature for f=p/q is bounded by kBTc(p/q)π|E₀(f)|2q. The resistance as a function of temperature and field is determined by the sequence of Tc's thus produced.
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Teitel et al. (1983) studied this question.
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