97,457 research outputs found
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
The statistical mechanics of thermally excited vortex lines with columnar
defects can be mapped onto the physics of interacting quantum particles with
quenched random disorder in one less dimension. The destruction of the Bose
glass phase in Type II superconductors, when the external magnetic field is
tilted sufficiently far from the column direction, is described by a poorly
understood non-Hermitian quantum phase transition. We present here exact
results for this transition in (1+1)-dimensions, obtained by mapping the
problem in the hard core limit onto one-dimensional fermions described by a
non-Hermitian tight binding model. Both site randomness and the relatively
unexplored case of bond randomness are considered. Analysis near the mobility
edge and near the band center in the latter case is facilitated by a real space
renormalization group procedure used previously for Hermitian quantum problems
with quenched randomness in one dimension.Comment: 23 pages, 22 figure
Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
We consider the effect of quenched spatial disorder on systems of
interacting, pinned non-Abelian anyons as might arise in disordered Hall
samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension,
such disordered anyon models have previously been shown to exhibit a hierarchy
of infinite randomness phases. Here, we address systems in two spatial
dimensions and report on the behavior of Ising and Fibonacci anyons under the
numerical strong-disorder renormalization group (SDRG). In order to manage the
topology-dependent interactions generated during the flow, we introduce a
planar approximation to the SDRG treatment. We characterize this planar
approximation by studying the flow of disordered hard-core bosons and the
transverse field Ising model, where it successfully reproduces the known
infinite randomness critical point with exponent \psi ~ 0.43. Our main
conclusion for disordered anyon models in two spatial dimensions is that
systems of Ising anyons as well as systems of Fibonacci anyons do not realize
infinite randomness phases, but flow back to weaker disorder under the
numerical SDRG treatment.Comment: 12 pages, 12 figures, 1 tabl
Strict Solution Method for Linear Programming Problem with Ellipsoidal Distributions under Fuzziness
This paper considers a linear programming problem with ellipsoidal distributions including fuzziness. Since this problem is not well-defined due to randomness and fuzziness, it is hard to solve it directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed model is transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve the main problem analytically and efficiently due to nonlinear programming, the solution method is constructed introducing an appropriate parameter and performing the equivalent transformations
Deep Spin-Glass Hysteresis Area Collapse and Scaling in the Ising Model
We investigate the dissipative loss in the Ising spin glass in three
dimensions through the scaling of the hysteresis area, for a maximum magnetic
field that is equal to the saturation field. We perform a systematic analysis
for the whole range of the bond randomness as a function of the sweep rate, by
means of frustration-preserving hard-spin mean field theory. Data collapse
within the entirety of the spin-glass phase driven adiabatically (i.e.,
infinitely-slow field variation) is found, revealing a power-law scaling of the
hysteresis area as a function of the antiferromagnetic bond fraction and the
temperature. Two dynamic regimes separated by a threshold frequency
characterize the dependence on the sweep rate of the oscillating field. For
, the hysteresis area is equal to its value in the adiabatic
limit , while for it increases with the
frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure
Numerical analysis of the magnetic-field-tuned superconductor-insulator transition in two dimensions
Ground state of the two-dimensional hard-core-boson model subjected to
external magnetic field and quenched random chemical potential is studied
numerically. In experiments, magnetic-field-tuned superconductor-insulator
transition has already come under through investigation, whereas in computer
simulation, only randomness-driven localization (with zero magnetic field) has
been studied so far: The external magnetic field brings about a difficulty that
the hopping amplitude becomes complex number (through the gauge twist), for
which the quantum Monte-Carlo simulation fails. Here, we employ the exact
diagonalization method, with which we demonstrate that the model does exhibit
field-tuned localization transition at a certain critical magnetic field. At
the critical point, we found that the DC conductivity is not universal, but is
substantially larger than that of the randomness-driven localization transition
at zero magnetic field. Our result supports recent experiment by Markovi'c et
al. reporting an increase of the critical conductivity with magnetic field
strengthened
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