11,525 research outputs found
Microscopic approach to orientational order of domain walls
We develop a fully microscopic, statistical mechanics approach to study phase
transitions in Ising systems with competing interactions at different scales.
Our aim is to consider orientational and positional order parameters in a
unified framework. In this work we consider two dimensional stripe forming
systems, where nematic, smectic and crystal phases are possible. We introduce a
nematic order parameter in a lattice, which measures orientational order of
interfaces. We develop a mean field approach which leads to a free energy which
is a function of both the magnetization (density) and the orientational
(nematic) order parameters. Self-consistent equations for the order parameters
are obtained and the solutions are described for a particular system, the
Dipolar Frustrated Ising Ferromagnet. We show that this system has an
Ising-nematic phase at low temperatures in the square lattice, where positional
order (staggered magnetization) is zero. At lower temperatures a crystal-stripe
phase may appear. In the continuum limit the present approach connects to a
Ginsburg-Landau theory, which has an isotropic-nematic phase transition with
breaking of a continuous symmetry.Comment: 9 pages, 7 figures, revised and expanded, published versio
Kinetically Inhibited Order in a Diamond-Lattice Antiferromagnet
Frustrated magnetic systems exhibit highly degenerate ground states and
strong fluctuations, often leading to new physics. An intriguing example of
current interest is the antiferromagnet on a diamond lattice, realized
physically in A-site spinel materials. This is a prototypical system in three
dimensions where frustration arises from competing interactions rather than
purely geometric constraints, and theory suggests the possibility of unusual
magnetic order at low temperature. Here we present a comprehensive
single-crystal neutron scattering study of CoAl2O4, a highly frustrated A-site
spinel. We observe strong diffuse scattering that peaks at wavevectors
associated with Neel ordering. Below the temperature T*=6.5 K, there is a
dramatic change in the elastic scattering lineshape accompanied by the
emergence of well-defined spin-wave excitations. T* had previously been
associated with the onset of glassy behavior. Our new results suggest instead
that T* signifies a first-order phase transition, but with true long-range
order inhibited by the kinetic freezing of domain walls. This scenario might be
expected to occur widely in frustrated systems containing first-order phase
transitions and is a natural explanation for existing reports of anomalous
glassy behavior in other materials.Comment: 40 pages, 9 figures, Introduction and discussion altered and
expanded. Additional section and figure added to Supplementary Informatio
On the defect induced gauge and Yukawa fields in graphene
We consider lattice deformations (both continuous and topological) in the
hexagonal lattice Hubbard model in the tight binding approximation to graphene,
involving operators with the range up to next-to-neighbor. In the low energy
limit, we find that these deformations give rise to couplings of the electronic
Dirac field to an external scalar (Yukawa) and gauge fields. The fields are
expressed in terms of original defects. As a by-product we establish that the
next-to-nearest order is the minimal range of deformations which produces the
complete gauge and scalar fields. We consider an example of Stone--Wales
defect, and find the associated gauge field.Comment: 21 pages, 2 figures, added the example of Stone-Wales defect,
presentation considerable improve
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Incremental learning of independent, overlapping, and graded concept descriptions with an instance-based process framework
Supervised learning algorithms make several simplifying assumptions concerning the characteristics of the concept descriptions to be learned. For example, concepts are often assumed to be (1) defined with respect to the same set of relevant attributes, (2) disjoint in instance space, and (3) have uniform instance distributions. While these assumptions constrain the learning task, they unfortunately limit an algorithm's applicability. We believe that supervised learning algorithms should learn attribute relevancies independently for each concept, allow instances to be members of any subset of concepts, and represent graded concept descriptions. This paper introduces a process framework for instance-based learning algorithms that exploit only specific instance and performance feedback information to guide their concept learning processes. We also introduce Bloom, a specific instantiation of this framework. Bloom is a supervised, incremental, instance-based learning algorithm that learns relative attribute relevancies independently for each concept, allows instances to be members of any subset of concepts, and represents graded concept memberships. We describe empirical evidence to support our claims that Bloom can learn independent, overlapping, and graded concept descriptions
Topology by Design in Magnetic nano-Materials: Artificial Spin Ice
Artificial Spin Ices are two dimensional arrays of magnetic, interacting
nano-structures whose geometry can be chosen at will, and whose elementary
degrees of freedom can be characterized directly. They were introduced at first
to study frustration in a controllable setting, to mimic the behavior of spin
ice rare earth pyrochlores, but at more useful temperature and field ranges and
with direct characterization, and to provide practical implementation to
celebrated, exactly solvable models of statistical mechanics previously devised
to gain an understanding of degenerate ensembles with residual entropy. With
the evolution of nano--fabrication and of experimental protocols it is now
possible to characterize the material in real-time, real-space, and to realize
virtually any geometry, for direct control over the collective dynamics. This
has recently opened a path toward the deliberate design of novel, exotic
states, not found in natural materials, and often characterized by topological
properties. Without any pretense of exhaustiveness, we will provide an
introduction to the material, the early works, and then, by reporting on more
recent results, we will proceed to describe the new direction, which includes
the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte
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Detecting and removing noisy instances from concept descriptions
Several published results show that instance-based learning algorithms record high classification accuracies and low storage requirements when applied to supervised learning tasks. However, these learning algorithms are highly sensitive to training set noise. This paper describes a simple extension of instance-based learning algorithms for detecting and removing noisy instances from concept descriptions. The extension requires evidence that saved instances be significantly good classifiers before it allows them to be used for subsequent classification tasks. We show that this extension's performance degrades more slowly in the presence of noise, improves classification accuracies, and further reduces storage requirements in several artificial and real-world databases
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