880 research outputs found
Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
We present a conjecture on the exact location of the multicritical point in
the phase diagram of spin glass models in finite dimensions. By generalizing
our previous work, we combine duality and gauge symmetry for replicated random
systems to derive formulas which make it possible to understand all the
relevant available numerical results in a unified way. The method applies to
non-self-dual lattices as well as to self dual cases, in the former case of
which we derive a relation for a pair of values of multicritical points for
mutually dual lattices. The examples include the +-J and Gaussian Ising spin
glasses on the square, hexagonal and triangular lattices, the Potts and Z_q
models with chiral randomness on these lattices, and the three-dimensional +-J
Ising spin glass and the random plaquette gauge model.Comment: 27 pages, 3 figure
Image restoration using the chiral Potts spin-glass
We report on the image reconstruction (IR) problem by making use of the
random chiral q-state Potts model, whose Hamiltonian possesses the same gauge
invariance as the usual Ising spin glass model. We show that the pixel
representation by means of the Potts variables is suitable for the gray-scale
level image which can not be represented by the Ising model. We find that the
IR quality is highly improved by the presence of a glassy term, besides the
usual ferromagnetic term under random external fields, as very recently pointed
out by Nishimori and Wong. We give the exact solution of the infinite range
model with q=3, the three gray-scale level case. In order to check our
analytical result and the efficiency of our model, 2D Monte Carlo simulations
have been carried out on real-world pictures with three and eight gray-scale
levels.Comment: RevTex 13 pages, 10 figure
Duality and Multicritical Point of Two-Dimensional Spin Glasses
Determination of the precise location of the multicritical point and phase
boundary is a target of active current research in the theory of spin glasses.
In this short note we develop a duality argument to predict the location of the
multicritical point and the shape of the phase boundary in models of spin
glasses on the square lattice.Comment: 4 pages, 1 figure; Reference updated, definition of \tilde{V} added;
to be published in J. Phys. Soc. Jp
Naive mean field approximation for image restoration
We attempt image restoration in the framework of the Baysian inference.
Recently, it has been shown that under a certain criterion the MAP (Maximum A
Posterior) estimate, which corresponds to the minimization of energy, can be
outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which
is equivalent to a finite-temperature decoding method. Since a lot of
computational time is needed for the MPM estimate to calculate the thermal
averages, the mean field method, which is a deterministic algorithm, is often
utilized to avoid this difficulty. We present a statistical-mechanical analysis
of naive mean field approximation in the framework of image restoration. We
compare our theoretical results with those of computer simulation, and
investigate the potential of naive mean field approximation.Comment: 9 pages, 11 figure
Tracing the Evolution of Physics on the Backbone of Citation Networks
Many innovations are inspired by past ideas in a non-trivial way. Tracing
these origins and identifying scientific branches is crucial for research
inspirations. In this paper, we use citation relations to identify the
descendant chart, i.e. the family tree of research papers. Unlike other
spanning trees which focus on cost or distance minimization, we make use of the
nature of citations and identify the most important parent for each
publication, leading to a tree-like backbone of the citation network. Measures
are introduced to validate the backbone as the descendant chart. We show that
citation backbones can well characterize the hierarchical and fractal structure
of scientific development, and lead to accurate classification of fields and
sub-fields.Comment: 6 pages, 5 figure
A Recursive Method of the Stochastic State Selection for Quantum Spin Systems
In this paper we propose the recursive stochastic state selection method, an
extension of the recently developed stochastic state selection method in Monte
Carlo calculations for quantum spin systems. In this recursive method we use
intermediate states to define probability functions for stochastic state
selections. Then we can diminish variances of samplings when we calculate
expectation values of the powers of the Hamiltonian. In order to show the
improvement we perform numerical calculations of the spin-1/2
anti-ferromagnetic Heisenberg model on the triangular lattice. Examining
results on the ground state of the 21-site system we confide this method in its
effectiveness. We also calculate the lowest and the excited energy eigenvalues
as well as the static structure factor for the 36-site system. The maximum
number of basis states kept in a computer memory for this system is about 3.6 x
10**7. Employing a translationally invariant initial trial state, we evaluate
the lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur
- …