Josephson-Junction Arrays in Transverse Magnetic Fields

Abstract

A class of uniformly frustrated $\mathrm{xy}$ 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 ${E}_{0}$ 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 $f=\frac{p}{q}$ is bounded by ${k}_{\mathrm{B}}{T}_{c}(\frac{p}{q})\ensuremath{\lesssim}\frac{\ensuremath{\pi}|{E}_{0}(f)|}{2q}$. The resistance as a function of temperature and field is determined by the sequence of ${T}_{c}$'s thus produced.