PHASE-TRANSITIONS IN JOSEPHSON-JUNCTION ARRAYS WITH LONG-RANGE INTERACTION

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 T(c) = NE(J)/2k(B) 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 T(c) = NE(J)/2k(B) square-root q. For the disordered case, T(c) can be defined in four different regions of f. For f < 1/N2, T(c) is similar to NE(J)/2k(B). For 1/N2 < f < 1/N, T(c) = E(J)/2k(B) square-root f, and for 1/N < f < 1, T(c) rises with increasing f, although the exact form is unknown at this time. For f > 1, T(c) asymptotically approaches approximately 0.85E(J) square-root N/k(B). Our Monte Carlo simulations confirm all of our analytical calculations, except that our simulations show that the high-field asymptote approaches approximately 0.75E(J) square-root N/k(B).