24,033 research outputs found
Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
We study the correlated-disorder driven zero-temperature phase transition of
the Random-Field Ising Magnet using exact numerical ground-state calculations
for cubic lattices. We consider correlations of the quenched disorder decaying
proportional to r^a, where r is the distance between two lattice sites and a<0.
To obtain exact ground states, we use a well established mapping to the
graph-theoretical maximum-flow problem, which allows us to study large system
sizes of more than two million spins. We use finite-size scaling analyses for
values a={-1,-2,-3,-7} to calculate the critical point and the critical
exponents characterizing the behavior of the specific heat, magnetization,
susceptibility and of the correlation length close to the critical point. We
find basically the same critical behavior as for the RFIM with delta-correlated
disorder, except for the finite-size exponent of the susceptibility and for the
case a=-1, where the results are also compatible with a phase transition at
infinitesimal disorder strength.
A summary of this work can be found at the papercore database at
www.papercore.org.Comment: 9 pages, 13 figure
Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
We perform Monte Carlo simulations of large two-dimensional Gaussian Ising
spin glasses down to very low temperatures . Equilibration is
ensured by using a cluster algorithm including Monte Carlo moves consisting of
flipping fundamental excitations. We study the thermodynamic behavior using the
Binder cumulant, the spin-glass susceptibility, the distribution of overlaps,
the overlap with the ground state and the specific heat. We confirm that
. All results are compatible with an algebraic divergence of the
correlation length with an exponent . We find , which
is compatible with the value for the domain-wall and droplet exponent
found previously in ground-state studies. Hence the
thermodynamic behavior of this model seems to be governed by one single
exponent.Comment: 7 pages, 11 figure
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D Random-Bond Ising Model
The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability of and of
are studied. We are able to consider large samples of up to
spins by using sophisticated matching algorithms. We study
systems, but we also consider samples, for different aspect ratios
. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region () are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at . Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding fixed. Here, large finite-size
effects are visible, which can be explained for all by a single exponent
, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for : the
distribution of the domain-wall energies converges to a Gaussian for ,
although the domain walls of neighboring subsystems of size are
not independent.Comment: 11 pages with 15 figures, extensively revise
RNA secondary structure design
We consider the inverse-folding problem for RNA secondary structures: for a
given (pseudo-knot-free) secondary structure find a sequence that has that
structure as its ground state. If such a sequence exists, the structure is
called designable. We implemented a branch-and-bound algorithm that is able to
do an exhaustive search within the sequence space, i.e., gives an exact answer
whether such a sequence exists. The bound required by the branch-and-bound
algorithm are calculated by a dynamic programming algorithm. We consider
different alphabet sizes and an ensemble of random structures, which we want to
design. We find that for two letters almost none of these structures are
designable. The designability improves for the three-letter case, but still a
significant fraction of structures is undesignable. This changes when we look
at the natural four-letter case with two pairs of complementary bases:
undesignable structures are the exception, although they still exist. Finally,
we also study the relation between designability and the algorithmic complexity
of the branch-and-bound algorithm. Within the ensemble of structures, a high
average degree of undesignability is correlated to a long time to prove that a
given structure is (un-)designable. In the four-letter case, where the
designability is high everywhere, the algorithmic complexity is highest in the
region of naturally occurring RNA.Comment: 11 pages, 10 figure
Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
We study ground-state properties of the two-dimensional random-bond Ising
model with couplings having a concentration of antiferromagnetic
and of ferromagnetic bonds. We apply an exact matching algorithm which
enables us the study of systems with linear dimension up to 700. We study
the behavior of the domain-wall energies and of the magnetization. We find that
the paramagnet-ferromagnet transition occurs at compared to
the concentration at the Nishimory point, which means that the
phase diagram of the model exhibits a reentrance. Furthermore, we find no
indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe
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
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
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