Two dynamic exponents in the resistive transition of fully frustrated Josephson-junction arrays

– We study the resistive transition in Josephson-junction arrays at f = 1/2 flux quantum per plaquette by dynamical simulations of the resistively-shunted-junction model. The current-voltage scaling and critical dynamics of the phases are found to be well described by the same critical temperature and static exponents as for the chiral (vortex-lattice) transition. Although this behavior is consistent with a single transition scenario, where phase and chiral variables order simultaneously, two different dynamic exponents result for phase coherence and chiral order. Phase transitions in two-dimensional Josephson junction arrays (JJA) has been a subject of much investigation [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. Such arrays can be artificially fabricated [1, 2, 3, 4] and are also closely related to superconducting wire networks [5, 6]. Experimentally, the resistive transition has been the one most extensively studied [2, 3, 4, 5, 6], while theoretically several studies of XY models [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], which describe the JJA, have been done. A significant understanding of these systems has already been achieved by comparing the experiments with the theoretically predicted equilibrium critical behavior with and without an applied magnetic field. However, to a large extent, dynamical critical behavior remains much less explored, particularly in the frustrated case (finite magnetic field). It is well known that while static critical phenomena depend on the spatial dimensionality as well as on the symmetry of the order parameter, the dynamic universality class will depend upon additional properties which do not affect the statics as, for example, conservation laws for the order parameter [30]. Thus, testing the universality hypothesis of dynamical critical behavior requires the study of specific dynamical models. In JJA, the physically relevant dynamical model for the phase dynamics has not been unambiguously identified [26, 27, 16, 17]. One would expect that, at least for an array of ideal tunnel junctions, the ResistivelyShunted-Junction (RSJ) model of current flow between superconducting grains would be a more physical representation of the system [28]. In experiments, the resistive transition in JJA is usually identified from the behavior of the current-voltage (I-V) characteristics near