355 research outputs found
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
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
Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm
We developed a genetic algorithm (GA) in the Heisenberg model that combines a
triadic crossover and a parameter-free genetic algorithm. Using the algorithm,
we examined the ground-state stiffness of the Heisenberg model in three
dimensions up to a moderate size range. Results showed the stiffness constant
of in the periodic-antiperiodic boundary condition method and that
of in the open-boundary-twist method. We considered the
origin of the difference in between the two methods and suggested that
both results show the same thing: the ground state of the open system is stable
against a weak perturbation.Comment: 11 pages, 5 figure
Ordered phase in the two-dimensional randomly coupled ferromagnet
True ground states are evaluated for a 2d Ising model with random near
neighbor interactions and ferromagnetic second neighbor interactions (the
Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive
when the absolute value of the random interaction is weaker than the
ferromagnetic interaction. This result demonstrates that in this parameter
domain the spin glass like ordering temperature is non-zero for these systems,
in strong contrast to the 2d Edwards-Anderson spin glass.Comment: 7 pages; 9 figures; revtex; new version much extende
Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions
We have studied low-lying metastable states of the Heisenberg model
in two () and three () dimensions having developed a hybrid genetic
algorithm. We have found a strong evidence of the occurrence of the Parisi
states in but not in . That is, in lattices, there exist
metastable states with a finite excitation energy of for
, and energy barriers between the ground state and
those metastable states are with in
but with in . We have also found droplet-like
excitations, suggesting a mixed scenario of the replica-symmetry-breaking
picture and the droplet picture recently speculated in the Ising SG model.Comment: 4 pages, 6 figure
Structure formation in binary colloids
A theoretical study of the structure formation observed very recently [Phys.
Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model
solely the dipole-dipole interaction of the particles is considered,
electrohidrodynamic effects are excluded. Based on molecular dynamics
simulations and analytic calculations we show that the total concentration of
the particles, the relative concentration and the relative dipole moment of the
components determine the structure of the colloid. At low concentrations the
kinetic aggregation of particles results in fractal structures which show a
crossover behavior when increasing the concentration. At high concentration
various lattice structures are obtained in a good agreement with experiments.Comment: revtex, 4 pages, figures available from authors due to size problem
Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
For many real spin-glass materials, the Edwards-Anderson model with
continuous-symmetry spins is more realistic than the rather better understood
Ising variant. In principle, the nature of an occurring spin-glass phase in
such systems might be inferred from an analysis of the zero-temperature
properties. Unfortunately, with few exceptions, the problem of finding
ground-state configurations is a non-polynomial problem computationally, such
that efficient approximation algorithms are called for. Here, we employ the
recently developed genetic embedded matching (GEM) heuristic to investigate the
nature of the zero-temperature phase of the bimodal XY spin glass in two
dimensions. We analyze bulk properties such as the asymptotic ground-state
energy and the phase diagram of disorder strength vs. disorder concentration.
For the case of a symmetric distribution of ferromagnetic and antiferromagnetic
bonds, we find that the ground state of the model is unique up to a global O(2)
rotation of the spins. In particular, there are no extensive degeneracies in
this model. The main focus of this work is on an investigation of the
excitation spectrum as probed by changing the boundary conditions. Using
appropriate finite-size scaling techniques, we consistently determine the
stiffness of spin and chiral domain walls and the corresponding fractal
dimensions. Most noteworthy, we find that the spin and chiral channels are
characterized by two distinct stiffness exponents and, consequently, the system
displays spin-chirality decoupling at large length scales. Results for the
overlap distribution do not support the possibility of a multitude of
thermodynamic pure states.Comment: 18 pages, RevTex 4, moderately revised version as publishe
Ground-state behavior of the 3d +/-J random-bond Ising model
Large numbers of ground states of the three-dimensional random-bond
Ising model are calculated for sizes up to using a combination of a
genetic algorithm and Cluster-Exact Approximation. Several quantities are
calculated as function of the concentration of the antiferromagnetic bonds.
The critical concentration where the ferromagnetic order disappears is
determined using the Binder cumulant of the magnetization. A value of
is obtained. From the finite-size behavior of the Binder
cumulant and the magnetization critical exponents and
are calculated.Comment: 8 pages, 11 figures, revte
On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
We compute and analyze couples of ground states of 3D spin glasses before and
after applying a volume perturbation which adds to the Hamiltonian a repulsion
from the true ground state. The physical picture based on Replica Symmetry
Breaking is in excellent agreement with the observed behavior.Comment: 4 pages including 5 .ps figure
Genetic embedded matching approach to ground states in continuous-spin systems
Due to an extremely rugged structure of the free energy landscape, the
determination of spin-glass ground states is among the hardest known
optimization problems, found to be NP-hard in the most general case. Owing to
the specific structure of local (free) energy minima, general-purpose
optimization strategies perform relatively poorly on these problems, and a
number of specially tailored optimization techniques have been developed in
particular for the Ising spin glass and similar discrete systems. Here, an
efficient optimization heuristic for the much less discussed case of continuous
spins is introduced, based on the combination of an embedding of Ising spins
into the continuous rotators and an appropriate variant of a genetic algorithm.
Statistical techniques for insuring high reliability in finding (numerically)
exact ground states are discussed, and the method is benchmarked against the
simulated annealing approach.Comment: 17 pages, 12 figures, 1 tabl
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