110 research outputs found
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
Spin glasses and algorithm benchmarks: A one-dimensional view
Spin glasses are paradigmatic models that deliver concepts relevant for a
variety of systems. However, rigorous analytical results are difficult to
obtain for spin-glass models, in particular for realistic short-range models.
Therefore large-scale numerical simulations are the tool of choice. Concepts
and algorithms derived from the study of spin glasses have been applied to
diverse fields in computer science and physics. In this work a one-dimensional
long-range spin-glass model with power-law interactions is discussed. The model
has the advantage over conventional systems in that by tuning the power-law
exponent of the interactions the effective space dimension can be changed thus
effectively allowing the study of large high-dimensional spin-glass systems to
address questions as diverse as the existence of an Almeida-Thouless line,
ultrametricity and chaos in short range spin glasses. Furthermore, because the
range of interactions can be changed, the model is a formidable test-bed for
optimization algorithms.Comment: 10 pages, 8 figures (two in crappy quality due to archive
restrictions). Proceedings of the International Workshop on
Statistical-Mechanical Informatics 2007, Kyoto (Japan) September 16-19, 200
Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
We use a nonperturbative extended contractor renormalization (ENCORE) method
for engineering quantum devices for the implementation of topologically
protected quantum bits described by an effective quantum dimer model on the
triangular lattice. By tuning the couplings of the device, topological
protection might be achieved if the ratio between effective two-dimer
interactions and flip amplitudes lies in the liquid phase of the phase diagram
of the quantum dimer model. For a proposal based on a quantum Josephson
junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503
(2002)] our results show that optimal operational temperatures below 1 mK can
only be obtained if extra interactions and dimer flips, which are not present
in the standard quantum dimer model and involve three or four dimers, are
included. It is unclear if these extra terms in the quantum dimer Hamiltonian
destroy the liquid phase needed for quantum computation. Minimizing the effects
of multi-dimer terms would require energy scales in the nano-Kelvin regime. An
alternative implementation based on cold atomic or molecular gases loaded into
optical lattices is also discussed, and it is shown that the small energy
scales involved--implying long operational times--make such a device
impractical. Given the many orders of magnitude between bare couplings in
devices, and the topological gap, the realization of topological phases in
quantum devices requires careful engineering and large bare interaction scales.Comment: 12 pages, 10 figure
Evolutionary Approaches to Optimization Problems in Chimera Topologies
Chimera graphs define the topology of one of the first commercially available
quantum computers. A variety of optimization problems have been mapped to this
topology to evaluate the behavior of quantum enhanced optimization heuristics
in relation to other optimizers, being able to efficiently solve problems
classically to use them as benchmarks for quantum machines. In this paper we
investigate for the first time the use of Evolutionary Algorithms (EAs) on
Ising spin glass instances defined on the Chimera topology. Three genetic
algorithms (GAs) and three estimation of distribution algorithms (EDAs) are
evaluated over hard instances of the Ising spin glass constructed from
Sidon sets. We focus on determining whether the information about the topology
of the graph can be used to improve the results of EAs and on identifying the
characteristics of the Ising instances that influence the success rate of GAs
and EDAs.Comment: 8 pages, 5 figures, 3 table
The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm
We study the efficiency of parallel tempering Monte Carlo technique for
calculating true ground states of the Edwards-Anderson spin glass model.
Bimodal and Gaussian bond distributions were considered in two and
three-dimensional lattices. By a systematic analysis we find a simple formula
to estimate the values of the parameters needed in the algorithm to find the GS
with a fixed average probability. We also study the performance of the
algorithm for single samples, quantifying the difference between samples where
the GS is hard, or easy, to find. The GS energies we obtain are in good
agreement with the values found in the literature. Our results show that the
performance of the parallel tempering technique is comparable to more powerful
heuristics developed to find the ground state of Ising spin glass systems.Comment: 30 pages, 17 figures. A new section added. Accepted for publication
in Physica
Reversal-field memory in magnetic hysteresis
We report results demonstrating a singularity in the hysteresis of magnetic
materials, the reversal-field memory effect. This effect creates a
nonanalyticity in the magnetization curves at a particular point related to the
history of the sample. The microscopic origin of the effect is associated with
a local spin-reversal symmetry of the underlying Hamiltonian. We show that the
presence or absence of reversal-field memory distinguishes two widely studied
models of spin glasses (random magnets).Comment: 3 pages, 5 figures. Proceedings of "2002 MMM Conferece", Tampa, F
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
Ordering of the Heisenberg Spin Glass in High Dimensions
Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian
coupling is investigated by equilibrium Monte Carlo simulations in four and
five dimensions. Ordering of the mean-field Heisenberg spin-glass is also
studied for comparison. Particular attention is paid to the nature of the
spin-glass and the chiral-glass orderings. Our numerical data suggest that, in
five dimensions, the model exhibits a single spin-glass transition at a finite
temperature, where the spin-glass order accompanying the simultaneous
chiral-glass order sets in. In four dimensions, by contrast, the model exhibits
a chiral-glass transition at a finite temperature, not accompanying the
standard spin-glass order. The critical region associated with the chiral-glass
transition, however, is very narrow, suggesting that dimension four is close to
the marginal dimensionality.Comment: 18 pages, 12 figure
Feedback-optimized parallel tempering Monte Carlo
We introduce an algorithm to systematically improve the efficiency of
parallel tempering Monte Carlo simulations by optimizing the simulated
temperature set. Our approach is closely related to a recently introduced
adaptive algorithm that optimizes the simulated statistical ensemble in
generalized broad-histogram Monte Carlo simulations. Conventionally, a
temperature set is chosen in such a way that the acceptance rates for replica
swaps between adjacent temperatures are independent of the temperature and
large enough to ensure frequent swaps. In this paper, we show that by choosing
the temperatures with a modified version of the optimized ensemble feedback
method we can minimize the round-trip times between the lowest and highest
temperatures which effectively increases the efficiency of the parallel
tempering algorithm. In particular, the density of temperatures in the
optimized temperature set increases at the "bottlenecks'' of the simulation,
such as phase transitions. In turn, the acceptance rates are now temperature
dependent in the optimized temperature ensemble. We illustrate the
feedback-optimized parallel tempering algorithm by studying the two-dimensional
Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and
briefly discuss possible feedback schemes for systems that require
configurational averages, such as spin glasses.Comment: 12 pages, 14 figure
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