Phase transitions in Josephson-junction arrays with long-range interaction

Abstract

We theoretically investigate ordered and disordered Josephson-junction arrays with long-range interaction. These arrays consist of two orthogonal sets of N parallel superconducting wires that are Josephson coupled to each other at every point of crossing. In this configuration, all wires, regardless of spatial separation, are nearest- or next-nearest neighbors. Using a mean-field approximation we show that the arrays undergo a phase transition to a macroscopically phase-coherent state at a temperature Tc=NEJ/2kB in the zero-field case. When a magnetic field, corresponding to a strongly commensurate number of flux quanta per unit cell, f=p/q, is introduced in an ordered array, we find that Tc=NEJ/2kB √q . For the disordered case, Tc can be defined in four different regions of f. For f<1/N2, Tc∼NEJ/2kB. For 1/N2<f<1/N, Tc=EJ/2kB √f , and for 1/N<f<1, Tc rises with increasing f, although the exact form is unknown at this time. For f>1, Tc asymptotically approaches ∼0.85EJ √N /kB. Our Monte Carlo simulations confirm all of our analytical calculations, except that our simulations show that the high-field asymptote approaches ∼0.75EJ √N /kB.

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