3,777 research outputs found
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
Compressible Sherrington-Kirkpatrick spin-glass model
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of
elastic degrees of freedom. The problem is formulated in terms of an effective
four-spin Hamiltonian in the pressure ensemble, which can be treated by the
replica method. In the replica-symmetric approximation, we analyze the
pressure-temperature phase diagram, and obtain expressions for the critical
boundaries between the disordered and the ordered (spin-glass and
ferromagnetic) phases. The second-order para-ferromagnetic border ends at a
tricritical point, beyond which the transition becomes discontinuous. We use
these results to make contact with the temperature-concentration phase diagrams
of mixtures of hydrogen-bonded crystals.Comment: 8 pages, 2 figures; added references, added conten
Spin-glass behaviour on random lattices
The ground-state phase diagram of an Ising spin-glass model on a random graph
with an arbitrary fraction of ferromagnetic interactions is analysed in the
presence of an external field. Using the replica method, and performing an
analysis of stability of the replica-symmetric solution, it is shown that
, correponding to an unbiased spin glass, is a singular point in the
phase diagram, separating a region with a spin-glass phase () from a
region with spin-glass, ferromagnetic, mixed, and paramagnetic phases
()
QuaSI: Quantile Sparse Image Prior for Spatio-Temporal Denoising of Retinal OCT Data
Optical coherence tomography (OCT) enables high-resolution and non-invasive
3D imaging of the human retina but is inherently impaired by speckle noise.
This paper introduces a spatio-temporal denoising algorithm for OCT data on a
B-scan level using a novel quantile sparse image (QuaSI) prior. To remove
speckle noise while preserving image structures of diagnostic relevance, we
implement our QuaSI prior via median filter regularization coupled with a Huber
data fidelity model in a variational approach. For efficient energy
minimization, we develop an alternating direction method of multipliers (ADMM)
scheme using a linearization of median filtering. Our spatio-temporal method
can handle both, denoising of single B-scans and temporally consecutive
B-scans, to gain volumetric OCT data with enhanced signal-to-noise ratio. Our
algorithm based on 4 B-scans only achieved comparable performance to averaging
13 B-scans and outperformed other current denoising methods.Comment: submitted to MICCAI'1
Spontaneous Symmetry Breakdown in non-relativistic Quantum Mechanics
The advantages and disadvantages of some pedagogical non-relativistic
quantum-mechanical models, used to illustrate spontaneous symmetry breakdown,
are discussed. A simple quantum-mechanical toy model (a spinor on the line,
subject to a magnetostatic interaction) is presented, that exhibits the
spontaneous breakdown of an internal symmetry.Comment: 19 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1111.1213. Equations (30) and (31) have been corrected. Other minor
correction
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