Revisiting the Theory of Finite Size Scaling in Disordered Systems: \nu Can Be Less Than 2/d

For phase transitions in disordered systems, an exact theorem provides a bound on the finite size correlation length exponent: \nu_{FS}<= 2/d. It is believed that the true critical exponent \nu of a disorder induced phase transition satisfies the same bound. We argue that in disordered systems the standard averaging introduces a noise, and a corresponding new diverging length scale, characterized by \nu_{FS}=2/d. This length scale, however, is independent of the system's own correlation length \xi. Therefore \nu can be less than 2/d. We illustrate these ideas on two exact examples, with \nu < 2/d. We propose a new method of disorder averaging, which achieves a remarkable noise reduction, and thus is able to capture the true exponents.Comment: 4 pages, Latex, one figure in .eps forma

Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model

We study hysteretic phenomena in random ferromagnets. We argue that the angle dependent magnetostatic (dipolar) terms introduce frustration and long range interactions in these systems. This makes it plausible that the Sherrington - Kirkpatrick model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations and large scale numerical simulations to characterize the hysteresis of the zero temperature SK model. By constructing the distribution functions of the avalanche sizes, magnetization jumps and local fields, we conclude that the system exhibits self-organized criticality everywhere on the hysteresis loop.Comment: 4 pages, 4 eps figure

Mean Field Theory of the Localization Transition

A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a uniform one. The inverse participation ratio, the single site Green's function, the superfluid order parameter and the corresponding susceptibility are calculated, and the appropriate exponents determined. All of these quantities indicate the presence of a new phase, which can be identified as the {\it Bose-glass}.Comment: 4 pages, Revtex, 2 figures appende

Direct Mott Insulator-to-Superfluid Transition in the Presence of Disorder

We introduce a new renormalization group theory to examine the quantum phase transitions upon exiting the insulating phase of a disordered, strongly interacting boson system. For weak disorder we find a direct transition from this Mott insulator to the Superfluid phase. In d > 4 a finite region around the particle-hole symmetric point supports this direct transition, whereas for 2=< d <4 perturbative arguments suggest that the direct transition survives only precisely at commensurate filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; first from the Mott insulator to the Bose glass, and then from the Bose glass to the Superfluid. The latter fixed point possesses statistical particle-hole symmetry and a dynamical exponent z, equal to the dimension d.Comment: 4 pages, Latex, submitted to Physical Review Letter

The Superconductor-Insulator Transition in a Tunable Dissipative Environment

We study the influence of a tunable dissipative environment on the dynamics of Josephson junction arrays near the superconductor-insulator transition. The experimental realization of the environment is a two dimensional electron gas coupled capacitively to the array. This setup allows for the well-controlled tuning of the dissipation by changing the resistance of the two dimensional electron gas. The capacitive coupling cuts off the dissipation at low frequencies. We determine the phase diagram and calculate the temperature and dissipation dependence of the array conductivity. We find good agreement with recent experimental results.Comment: 4 pages, 4 .eps figures, revte

Phase-Locking of Vortex Lattices Interacting with Periodic Pinning

We examine Shapiro steps for vortex lattices interacting with periodic pinning arrays driven by AC and DC currents. The vortex flow occurs by the motion of the interstitial vortices through the periodic potential generated by the vortices that remain pinned at the pinning sites. Shapiro steps are observed for fields B_{\phi} < B < 2.25B_{\phi} with the most pronouced steps occuring for fields where the interstitial vortex lattice has a high degree of symmetry. The widths of the phase-locked current steps as a function of the magnitude of the AC driving are found to follow a Bessel function in agreement with theory.Comment: 5 pages 5 postscript figure

The Phase Diagram of Disordered Vortices from London Langevin Simulations

We study the phase diagram of vortex matter in disordered type-II superconductors. We performed numerical simulations in the London Langevin approximation, using a new realistic representation of the disorder. At low magnetic fields we find a disentangled and dislocation free Bragg-glass regime. Increasing the field introduces disorder-driven entanglement in a discontinuous manner, leading to a vortex-glass phase, which subsequently melts into the vortex liquid. The obtained phase boundaries are in quantitative agreement with the experimental data.Comment: 4 pages, revtex, 8 postscript figures include

Reply to the Comment on 'Quantum Phase Slips and Transport in Ultra-Thin Superconducting Wires'

We reply to the recent Comment [cond-mat/9702231] by J.-M. Duan. Our point of view is markedly different on every issue raised. Much of the disagreement can be traced to a different preception of experimentally relevant length scales. i) We explain the difference between our formulation, which rests on a microscopic basis, and the phenomenological one of the author. ii) Our renormalization scheme is fundamentally right, as the "log(log)" interaction appears only in wires of astronomical lengths. iii) The tunneling barrier is profoundly reduced by the kinetic inductance. iv) We do make an appropriate comparison to the data on the thinnest available wires.Comment: 1 page Revte