18,169 research outputs found
Reduction of Two-Dimensional Dilute Ising Spin Glasses
The recently proposed reduction method is applied to the Edwards-Anderson
model on bond-diluted square lattices. This allows, in combination with a
graph-theoretical matching algorithm, to calculate numerically exact ground
states of large systems. Low-temperature domain-wall excitations are studied to
determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found,
consistent with previous results obtained on undiluted lattices. This
comparison demonstrates the validity of the reduction method for bond-diluted
spin systems and provides strong support for similar studies proclaiming
accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see
http://www.physics.emory.edu/faculty/boettcher
A new method for analyzing ground-state landscapes: ballistic search
A ``ballistic-search'' algorithm is presented which allows the identification
of clusters (or funnels) of ground states in Ising spin glasses even for
moderate system sizes. The clusters are defined to be sets of states, which are
connected in state-space by chains of zero-energy flips of spins. The technique
can also be used to estimate the sizes of such clusters. The performance of the
method is tested with respect to different system sizes and choices of
parameters. As an application the ground-state funnel structure of
two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by
calculating a huge number of ground states per realization. A T=0 entropy per
spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte
Universality-class dependence of energy distributions in spin glasses
We study the probability distribution function of the ground-state energies
of the disordered one-dimensional Ising spin chain with power-law interactions
using a combination of parallel tempering Monte Carlo and branch, cut, and
price algorithms. By tuning the exponent of the power-law interactions we are
able to scan several universality classes. Our results suggest that mean-field
models have a non-Gaussian limiting distribution of the ground-state energies,
whereas non-mean-field models have a Gaussian limiting distribution. We compare
the results of the disordered one-dimensional Ising chain to results for a
disordered two-leg ladder, for which large system sizes can be studied, and
find a qualitative agreement between the disordered one-dimensional Ising chain
in the short-range universality class and the disordered two-leg ladder. We
show that the mean and the standard deviation of the ground-state energy
distributions scale with a power of the system size. In the mean-field
universality class the skewness does not follow a power-law behavior and
converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick
model seem to be acceptably well fitted by a modified Gumbel distribution.
Finally, we discuss the distribution of the internal energy of the
Sherrington-Kirkpatrick model at finite temperatures and show that it behaves
similar to the ground-state energy of the system if the temperature is smaller
than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl
On Which Length Scales Can Temperature Exist in Quantum Systems?
We consider a regular chain of elementary quantum systems with nearest
neighbor interactions and assume that the total system is in a canonical state
with temperature . We analyze under what condition the state factors into a
product of canonical density matrices with respect to groups of subsystems
each, and when these groups have the same temperature . While in classical
mechanics the validity of this procedure only depends on the size of the groups
, in quantum mechanics the minimum group size also depends
on the temperature ! As examples, we apply our analysis to different types
of Heisenberg spin chains.Comment: To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn.
74 (2005) Supp
On the merit of a Central Limit Theorem-based approximation in statistical physics
The applicability conditions of a recently reported Central Limit
Theorem-based approximation method in statistical physics are investigated and
rigorously determined. The failure of this method at low and intermediate
temperature is proved as well as its inadequacy to disclose quantum
criticalities at fixed temperatures. Its high temperature predictions are in
addition shown to coincide with those stemming from straightforward appropriate
expansions up to (k_B T)^(-2). Our results are clearly illustrated by comparing
the exact and approximate temperature dependence of the free energy of some
exemplary physical systems.Comment: 12 pages, 1 figur
Iterative Perturbation Theory for Strongly Correlated Electron Systems with Orbital Degeneracy
A new scheme of the iterative perturbation theory is proposed for the
strongly correlated electron systems with orbital degeneracy. The method is
based on the modified self-energy of Yeyati, et al. which interpolates between
the weak and the strong correlation limits, but a much simpler scheme is
proposed which is useful in the case of the strong correlation with orbital
degeneracy. It will be also useful in the study of the electronic structures
combined with the band calculations.Comment: 6 pages, 3 Postscript figures, to appear in J. Phys. Cond. Matte
Advanced flight control system study
A fly by wire flight control system architecture designed for high reliability includes spare sensor and computer elements to permit safe dispatch with failed elements, thereby reducing unscheduled maintenance. A methodology capable of demonstrating that the architecture does achieve the predicted performance characteristics consists of a hierarchy of activities ranging from analytical calculations of system reliability and formal methods of software verification to iron bird testing followed by flight evaluation. Interfacing this architecture to the Lockheed S-3A aircraft for flight test is discussed. This testbed vehicle can be expanded to support flight experiments in advanced aerodynamics, electromechanical actuators, secondary power systems, flight management, new displays, and air traffic control concepts
Scaling of stiffness energy for 3d +/-J Ising spin glasses
Large numbers of ground states of 3d EA Ising spin glasses are calculated for
sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact
Approximation. A detailed analysis shows that true ground states are obtained.
The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t
behavior with t=0.19(2) is found which strongly indicates that the 3d model has
an equilibrium spin-glass-paramagnet transition for non-zero T_c.Comment: 4 pages, 4 figure
Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
We investigate the performance of flat-histogram methods based on a
multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional
+/- J spin glass by measuring round-trip times in the energy range between the
zero-temperature ground state and the state of highest energy. Strong
sample-to-sample variations are found for fixed system size and the
distribution of round-trip times follows a fat-tailed Frechet extremal value
distribution. Rare events in the fat tails of these distributions corresponding
to extremely slowly equilibrating spin glass realizations dominate the
calculations of statistical averages. While the typical round-trip time scales
exponential as expected for this NP-hard problem, we find that the average
round-trip time is no longer well-defined for systems with N >= 8^3 spins. We
relate the round-trip times for multicanonical sampling to intrinsic properties
of the energy landscape and compare with the numerical effort needed by the
genetic Cluster-Exact Approximation to calculate the exact ground state
energies. For systems with N >= 8^3 spins the simulation of these rare events
becomes increasingly hard. For N >= 14^3 there are samples where the
Wang-Landau algorithm fails to find the true ground state within reasonable
simulation times. We expect similar behavior for other algorithms based on
multicanonical sampling.Comment: 9 pages, 12 figure
Fully Frustrated Ising System on a 3D Simple Cubic Lattice: Revisited
Using extensive Monte Carlo simulations, we clarify the critical behaviour of
the 3 dimensional simple cubic Ising Fully Frustrated system. We find two
transition temperatures and two long range ordered phases. Within the present
numerical accuracy, the transition at higher temperature is found to be second
order and we have extracted the standard critical exponent using finite size
scaling method. On the other hand, the transition at lower temperature is found
to be first order. It is argued that entropy plays a major role on determining
the low temperature state.Comment: 14 pages 14 figures iop style include
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