928 research outputs found
Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2
Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
A huge number of independent true ground-state configurations is calculated
for two-, three- and four-dimensional +- J spin-glass models. Using the genetic
cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are
treated. A ``ballistic-search'' algorithm is applied which allows even for
large system sizes to identify clusters of ground states which are connected by
chains of zero-energy flips of spins. The number of clusters n_C diverges with
N going to infinity. For all dimensions considered here, an exponential
increase of n_C appears to be more likely than a growth with a power of N. The
number of different ground states is found to grow clearly exponentially with
N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B
(3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference
Low-energy excitations in the three-dimensional random-field Ising model
The random-field Ising model (RFIM), one of the basic models for quenched
disorder, can be studied numerically with the help of efficient ground-state
algorithms. In this study, we extend these algorithm by various methods in
order to analyze low-energy excitations for the three-dimensional RFIM with
Gaussian distributed disorder that appear in the form of clusters of connected
spins. We analyze several properties of these clusters. Our results support the
validity of the droplet-model description for the RFIM.Comment: 10 pages, 9 figure
Calculation of ground states of four-dimensional +or- J Ising spin glasses
Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated
for sizes up to 7x7x7x7 using a combination of a genetic algorithm and
cluster-exact approximation. The ground-state energy of the infinite system is
extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)
energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found
which confirms that the d=4 model has an equilibrium spin-glass-paramagnet
transition for non-zero T_c.Comment: 5 pages, 3 figures, 31 references, revtex; update of reference
No spin-glass transition in the "mobile-bond" model
The recently introduced ``mobile-bond'' model for two-dimensional spin
glasses is studied. The model is characterized by an annealing temperature T_q.
On the basis of Monte Carlo simulations of small systems it has been claimed
that this model exhibits a non-trivial spin-glass transition at finite
temperature for small values of T_q.
Here the model is studied by means of exact ground-state calculations of
large systems up to N=256^2. The scaling of domain-wall energies is
investigated as a function of the system size. For small values T_q<0.95 the
system behaves like a (gauge-transformed) ferromagnet having a small fraction
of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard
two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at
T>0.Comment: 4 pages, 5 figures, RevTe
Lower Critical Dimension of Ising Spin Glasses
Exact ground states of two-dimensional Ising spin glasses with Gaussian and
bimodal (+- J) distributions of the disorder are calculated using a
``matching'' algorithm, which allows large system sizes of up to N=480^2 spins
to be investigated. We study domain walls induced by two rather different types
of boundary-condition changes, and, in each case, analyze the system-size
dependence of an appropriately defined ``defect energy'', which we denote by
DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with
\theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition
changes. These results are in reasonable agreement with each other, allowing
for small systematic effects. They also agree well with earlier work on smaller
sizes. The negative value indicates that two dimensions is below the lower
critical dimension d_c. For the +-J model, we obtain a different result, namely
the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta
= 0, indicating that the lower critical dimension for the +-J model exactly
d_c=2.Comment: 4 pages, 4 figures, 1 table, revte
A dedicated algorithm for calculating ground states for the triangular random bond Ising model
In the presented article we present an algorithm for the computation of
ground state spin configurations for the 2d random bond Ising model on planar
triangular lattice graphs. Therefore, it is explained how the respective ground
state problem can be mapped to an auxiliary minimum-weight perfect matching
problem, solvable in polynomial time. Consequently, the ground state properties
as well as minimum-energy domain wall (MEDW) excitations for very large 2d
systems, e.g. lattice graphs with up to N=384x384 spins, can be analyzed very
fast. Here, we investigate the critical behavior of the corresponding T=0
ferromagnet to spin-glass transition, signaled by a breakdown of the
magnetization, using finite-size scaling analyses of the magnetization and MEDW
excitation energy and we contrast our numerical results with previous
simulations and presumably exact results.Comment: 5 pages, 5 figure
Generating droplets in two-dimensional Ising spin glasses by using matching algorithms
We study the behavior of droplets for two dimensional Ising spin glasses with
Gaussian interactions. We use an exact matching algorithm which enables study
of systems with linear dimension L up to 240, which is larger than is possible
with other approaches. But the method only allows certain classes of droplets
to be generated. We study single-bond, cross and a category of fixed volume
droplets as well as first excitations. By comparison with similar or equivalent
droplets generated in previous works, the advantages but also the limitations
of this approach are revealed. In particular we have studied the scaling
behavior of the droplet energies and droplet sizes. In most cases, a crossover
of the data can be observed such that for large sizes the behavior is
compatible with the one-exponent scenario of the droplet theory. Only for the
case of first excitations, no clear conclusion can be reached, probably because
even with the matching approach the accessible system sizes are still too
small.Comment: 11 pages, 16 figures, revte
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Scaling and self-averaging in the three-dimensional random-field Ising model
We investigate, by means of extensive Monte Carlo simulations, the magnetic
critical behavior of the three-dimensional bimodal random-field Ising model at
the strong disorder regime. We present results in favor of the two-exponent
scaling scenario, , where and are the
critical exponents describing the power-law decay of the connected and
disconnected correlation functions and we illustrate, using various finite-size
measures and properly defined noise to signal ratios, the strong violation of
self-averaging of the model in the ordered phase.Comment: 8 pages, 6 figures, to be published in Eur. Phys. J.
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