31 research outputs found
Casimir Force between two Half Spaces of Vortex Matter in Anisotropic Superconductors
We present a new approach to calculate the attractive long-range
vortex-vortex interaction of the van der Waals type present in anisotropic and
layered superconductors. The mapping of the statistical mechanics of
two-dimensional charged bosons allows us to define a Casimir problem: Two half
spaces of vortex matter separated by a gap of width R are mapped to two
dielectric half planes of charged bosons interacting via a massive gauge field.
We determine the attractive Casimir force between the two half planes and show
that it agrees with the pairwise summation of the van der Waals force between
vortices.Comment: Submitted to Physica C (4 pages, 2 figures
On the existence of a finite-temperature transition in the two-dimensional gauge glass
Results from Monte Carlo simulations of the two-dimensional gauge glass
supporting a zero-temperature transition are presented. A finite-size scaling
analysis of the correlation length shows that the system does not exhibit
spin-glass order at finite temperatures. These results are compared to earlier
claims of a finite-temperature transition.Comment: 4 pages, 2 figure
Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures
We report results for simulations of the four-dimensional XY spin glass using
the parallel tempering Monte Carlo method at low temperatures for moderate
sizes. Our results are qualitatively consistent with earlier work on the
three-dimensional gauge glass as well as three- and four-dimensional
Edwards-Anderson Ising spin glass. An extrapolation of our results would
indicate that large-scale excitations cost only a finite amount of energy in
the thermodynamic limit. The surface of these excitations may be fractal,
although we cannot rule out a scenario compatible with replica symmetry
breaking in which the surface of low-energy large-scale excitations is space
filling.Comment: 6 pages, 8 figure
Numerical studies of the two- and three-dimensional gauge glass at low temperature
We present results from Monte Carlo simulations of the two- and
three-dimensional gauge glass at low temperature using the parallel tempering
Monte Carlo method. Our results in two dimensions strongly support the
transition being at T_c=0. A finite-size scaling analysis, which works well
only for the larger sizes and lower temperatures, gives the stiffness exponent
theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01,
compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR
Zero Temperature Glass Transition in the Two-Dimensional Gauge Glass Model
We investigate dynamic scaling properties of the two-dimensional gauge glass
model for the vortex glass phase in superconductors with quenched disorder.
From extensive Monte Carlo simulations we obtain static and dynamic finite
size scaling behavior, where the static simulations use a temperature exchange
method to ensure convergence at low temperatures. Both static and dynamic
scaling of Monte Carlo data is consistent with a glass transition at zero
temperature. We study a dynamic correlation function for the superconducting
order parameter, as well as the phase slip resistance. From the scaling of
these two functions, we find evidence for two distinct diverging correlation
times at the zero temperature glass transition. The longer of these time scales
is associated with phase slip fluctuations across the system that lead to
finite resistance at any finite temperature, while the shorter time scale is
associated with local phase fluctuations.Comment: 8 pages, 10 figures; v2: some minor correction
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Nature of the Spin-glass State in the Three-dimensional Gauge Glass
We present results from simulations of the gauge glass model in three
dimensions using the parallel tempering Monte Carlo technique. Critical
fluctuations should not affect the data since we equilibrate down to low
temperatures, for moderate sizes. Our results are qualitatively consistent with
earlier work on the three and four dimensional Edwards-Anderson Ising spin
glass. We find that large scale excitations cost only a finite amount of energy
in the thermodynamic limit, and that those excitations have a surface whose
fractal dimension is less than the space dimension, consistent with a scenario
proposed by Krzakala and Martin, and Palassini and Young.Comment: 5 pages, 7 figure
Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering
Parallel tempering and population annealing are both effective methods for
simulating equilibrium systems with rough free energy landscapes. Parallel
tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte
Carlo method while population annealing is a sequential Monte Carlo method.
Both methods overcome the exponential slowing associated with high free energy
barriers. The convergence properties and efficiency of the two methods are
compared. For large systems, population annealing initially converges to
equilibrium more rapidly than parallel tempering for the same amount of
computational work. However, parallel tempering converges exponentially and
population annealing inversely in the computational work so that ultimately
parallel tempering approaches equilibrium more rapidly than population
annealing.Comment: 10 pages, 3 figure
Equilibrium valleys in spin glasses at low temperature
We investigate the 3-dimensional Edwards-Anderson spin glass model at low
temperature on simple cubic lattices of sizes up to L=12. Our findings show a
strong continuity among T>0 physical features and those found previously at
T=0, leading to a scenario with emerging mean field like characteristics that
are enhanced in the large volume limit. For instance, the picture of space
filling sponges seems to survive in the large volume limit at T>0, while
entropic effects play a crucial role in determining the free-energy degeneracy
of our finite volume states. All of our analysis is applied to equilibrium
configurations obtained by a parallel tempering on 512 different disorder
realizations. First, we consider the spatial properties of the sites where
pairs of independent spin configurations differ and we introduce a modified
spin overlap distribution which exhibits a non-trivial limit for large L.
Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations
into valleys. On average these valleys have free-energy differences of O(1),
but a difference in the (extensive) internal energy that grows significantly
with L; there is thus a large interplay between energy and entropy
fluctuations. We also find that valleys typically differ by sponge-like space
filling clusters, just as found previously for low-energy system-size
excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional
reference
Structure of 2D Topological Stabilizer Codes
We provide a detailed study of the general structure of two-dimensional
topological stabilizer quantum error correcting codes, including subsystem
codes. Under the sole assumption of translational invariance, we show that all
such codes can be understood in terms of the homology of string operators that
carry a certain topological charge. In the case of subspace codes, we prove
that two codes are equivalent under a suitable set of local transformations if
and only they have equivalent topological charges. Our approach emphasizes
local properties of the codes over global ones.Comment: 54 pages, 11 figures, version accepted in journal, improved
presentation and result