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

Reversal-Field Memory in the Hysteresis of Spin Glasses

We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a non-analyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use First Order Reversal Curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films. We contrast our results on spin glasses to random magnets and show that the FORC technique is an effective "magnetic fingerprinting" tool.Comment: 4 pages, 6 figure

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

Hysteretic Optimization

We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is endowed with a suitable `distance'. We test the new algorithm on frustrated magnetic models and the traveling salesman problem. We find that the new method successfully competes with similar basic algorithms such as simulated annealing.Comment: 5 pages, 5 figure

Anomalous Quantum Diffusion at the Superfluid-Insulator Transition

We consider the problem of the superconductor-insulator transition in the presence of disorder, assuming that the fermionic degrees of freedom can be ignored so that the problem reduces to one of Cooper pair localization. Weak disorder drives the critical behavior away from the pure critical point, initially towards a diffusive fixed point. We consider the effects of Coulomb interactions and quantum interference at this diffusive fixed point. Coulomb interactions enhance the conductivity, in contrast to the situation for fermions, essentially because the exchange interaction is opposite in sign. The interaction-driven enhancement of the conductivity is larger than the weak-localization suppression, so the system scales to a perfect conductor. Thus, it is a consistent possibility for the critical resistivity at the superconductor-insulator transition to be zero, but this value is only approached logarithmically. We determine the values of the critical exponents $\eta,z,\nu$ and comment on possible implications for the interpretation of experiments

Quantum critical phenomena of long-range interacting bosons in a time-dependent random potential

We study the superfluid-insulator transition of a particle-hole symmetric system of long-range interacting bosons in a time-dependent random potential in two dimensions, using the momentum-shell renormalization-group method. We find a new stable fixed point with non-zero values of the parameters representing the short- and long-range interactions and disorder when the interaction is asymptotically logarithmic. This is contrasted to the non-random case with a logarithmic interaction, where the transition is argued to be first-order, and to the $1/r$ Coulomb interaction case, where either a first-order transition or an XY-like transition is possible depending on the parameters. We propose that our model may be relevant in studying the vortex liquid-vortex glass transition of interacting vortex lines in point-disordered type-II superconductors.Comment: 10 pages, 3 figure

On the statistical mechanics of prion diseases

We simulate a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., Mad Cow disease) with concommitant prion protein misfolding and aggregation. Our simulations lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self averaging. We model `species barriers' to prion infection and assess a related treatment protocol.Comment: 5 Pages, 3 eps figures (submitted to Physical Review Letters

Critical behavior at superconductor-insulator phase transitions near one dimension

I argue that the system of interacting bosons at zero temperature and in random external potential possesses a simple critical point which describes the proliferation of disorder-induced topological defects in the superfluid ground state, and which is located at weak disorder close to and above one dimension. This makes it possible to address the critical behavior at the superfluid-Bose glass transition in dirty boson systems by expanding around the lower critical dimension d=1. Within the formulated renormalization procedure near d=1 the dynamical critical exponent is obtained exactly and the correlation length exponent is calculated as a Laurent series in the parameter \sqrt{\epsilon}, with \epsilon=d-1: z=d, \nu=1/\sqrt{3\epsilon} for the short range, and z=1, \nu=\sqrt{2/3\epsilon}, for the long-range Coulomb interaction between bosons. The identified critical point should be stable against the residual perturbations in the effective action for the superfluid, at least in dimensions 1\leq d \leq 2, for both short-range and Coulomb interactions. For the superfluid-Mott insulator transition in the system in a periodic potential and at a commensurate density of bosons I find \nu=(1/2\sqrt{\epsilon})+ 1/4+O(\sqrt{\epsilon}), which yields a result reasonably close to the known XY critical exponent in d=2+1. The critical behavior of the superfluid density, phonon velocity and the compressibility in the system with the short-range interactions is discussed.Comment: 23 pages, 1 Postscript figure, LaTe

On the Finite Size Scaling in Disordered Systems

The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension $d=4-\epsilon$ and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.Comment: 21 pages, 2 figures, submitted to the Physcal Review

Phase diagram of a Disordered Boson Hubbard Model in Two Dimensions

We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram of this model is constructed in terms of the disorder strength and the chemical potential. Via quantum Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where a random potential is irrelevant, from the strong-disorder regime. In the weak-disorder regime, the Mott-insulator-to-superfluid transition occurs, while, in the strong-disorder regime, the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z=1.35 \pm 0.05$ and the correlation length critical exponent $\nu=0.67 \pm 0.03$, that are different from the values for the transitions off the line. We suggest that the proliferation of the particle-hole pairs screens out the weak disorder effects.Comment: 4 pages, 4 figures, to be published in PR