20,634 research outputs found
Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension
The disorder-driven phase transition of the RFIM is observed using exact
ground-state computer simulations for hyper cubic lattices in d=5,6,7
dimensions. Finite-size scaling analyses are used to calculate the critical
point and the critical exponents of the specific heat, magnetization,
susceptibility and of the correlation length. For dimensions d=6,7 which are
larger or equal to the assumed upper critical dimension, d_u=6, mean-field
behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis
of the numerical data, it appears to be necessary to include recently proposed
corrections to scaling at and beyond the upper critical dimension.Comment: 8 pages and 13 figures; A consise summary of this work can be found
in the papercore database at http://www.papercore.org/Ahrens201
Large-deviation properties of the extended Moran model
The distributions of the times to the first common ancestor t_mrca is
numerically studied for an ecological population model, the extended Moran
model. This model has a fixed population size N. The number of descendants is
drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of
alpha. This includes also the classical Moran model (alpha->0) as well as the
uniform distribution (alpha=1). Using a statistical mechanics-based
large-deviation approach, the distributions can be studied over an extended
range of the support, down to probabilities like 10^{-70}, which allowed us to
study the change of the tails of the distribution when varying the value of
alpha in [0,2]. We find exponential distributions p(t_mrca)~ delta^{t_mrca} in
all cases, with systematically varying values for the base delta. Only for the
cases alpha=0 and alpha=1, analytical results are known, i.e.,
delta=\exp(-2/N^2) and delta=2/3, respectively. We recover these values,
confirming the validity of our approach. Finally, we also study the
correlations between t_mrca and the number of descendants.Comment: 8 pages, 8 figure
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
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
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
Optimal Vertex Cover for the Small-World Hanoi Networks
The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with
an exact renormalization group and parallel-tempering Monte Carlo simulations.
The grand canonical partition function of the equivalent hard-core repulsive
lattice-gas problem is recast first as an Ising-like canonical partition
function, which allows for a closed set of renormalization group equations. The
flow of these equations is analyzed for the limit of infinite chemical
potential, at which the vertex-cover problem is attained. The relevant fixed
point and its neighborhood are analyzed, and non-trivial results are obtained
both, for the coverage as well as for the ground state entropy density, which
indicates the complex structure of the solution space. Using special
hierarchy-dependent operators in the renormalization group and Monte-Carlo
simulations, structural details of optimal configurations are revealed. These
studies indicate that the optimal coverages (or packings) are not related by a
simple symmetry. Using a clustering analysis of the solutions obtained in the
Monte Carlo simulations, a complex solution space structure is revealed for
each system size. Nevertheless, in the thermodynamic limit, the solution
landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final
version; for related information, see
http://www.physics.emory.edu/faculty/boettcher
Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses
Unbiased samples of ground states were generated for the short-range Ising
spin glass with Jij=+/-1, in three dimensions. Clustering the ground states
revealed their hierarchical structure, which is explained by correlated spin
domains, serving as cores for macroscopic zero energy "excitations".Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let
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
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