169 research outputs found
Finite size scaling of the bayesian perceptron
We study numerically the properties of the bayesian perceptron through a
gradient descent on the optimal cost function. The theoretical distribution of
stabilities is deduced. It predicts that the optimal generalizer lies close to
the boundary of the space of (error-free) solutions. The numerical simulations
are in good agreement with the theoretical distribution. The extrapolation of
the generalization error to infinite input space size agrees with the
theoretical results. Finite size corrections are negative and exhibit two
different scaling regimes, depending on the training set size. The variance of
the generalization error vanishes for confirming the
property of self-averaging.Comment: RevTeX, 7 pages, 7 figures, submitted to Phys. Rev.
Switching of the magnetic order in CeRhInSn in the vicinity of its quantum critical point
We report neutron diffraction experiments performed in the tetragonal
antiferromagnetic heavy fermion system CeRhInSn in its (, )
phase diagram up to the vicinity of the critical concentration
0.40, where long range magnetic order is suppressed. The propagation vector of
the magnetic structure is found to be =(1/2, 1/2, ) with
increasing from =0.298 to =0.410 when increases from =0
to =0.26. Surprisingly, for =0.30, the order has changed drastically and
a commensurate antiferromagnetism with =(1/2, 1/2, 0) is found.
This concentration is located in the proximity of the quantum critical point
where superconductivity is expected.Comment: 5 pages, 5 figures, submitted to Phys. Rev.
Kovacs effect and fluctuation-dissipation relations in 1D kinetically constrained models
Strong and fragile glass relaxation behaviours are obtained simply changing
the constraints of the kinetically constrained Ising chain from symmetric to
purely asymmetric. We study the out-of-equilibrium dynamics of those two models
focusing on the Kovacs effect and the fluctuation--dissipation relations. The
Kovacs or memory effect, commonly observed in structural glasses, is present
for both constraints but enhanced with the asymmetric ones. Most surprisingly,
the related fluctuation-dissipation (FD) relations satisfy the FD theorem in
both cases. This result strongly differs from the simple quenching procedure
where the asymmetric model presents strong deviations from the FD theorem.Comment: 13 pages and 7 figures. To be published in J. Phys.
A Tale of Two Metals: contrasting criticalities in the pnictides and hole-doped cuprates
The iron-based high temperature superconductors share a number of
similarities with their copper-based counterparts, such as reduced
dimensionality, proximity to states of competing order, and a critical role for
3d electron orbitals. Their respective temperature-doping phase diagrams also
contain certain commonalities that have led to claims that the metallic and
superconducting properties of both families are governed by their proximity to
a quantum critical point (QCP) located inside the superconducting dome. In this
review, we critically examine these claims and highlight significant
differences in the bulk physical properties of both systems. While there is now
a large body of evidence supporting the presence of a (magnetic) QCP in the
iron pnictides, the situation in the cuprates is much less apparent, at least
for the end point of the pseudogap phase. We argue that the opening of the
normal state pseudogap in cuprates, so often tied to a putative QCP, arises
from a momentum-dependent breakdown of quasiparticle coherence that sets in at
much higher doping levels but which is driven by the proximity to the Mott
insulating state at half filling. Finally, we present a new scenario for the
cuprates in which this loss of quasiparticle integrity and its evolution with
momentum, temperature and doping plays a key role in shaping the resultant
phase diagram.Comment: This key issues review is dedicated to the memory of Dr. John Loram
whose pioneering measurements, analysis and ideas inspired much of its
conten
Optical conductivity of URuSi in the Kondo Liquid and Hidden-Order Phases
We measured the polarized optical conductivity of URuSi from room
temperature down to 5 K, covering the Kondo state, the coherent Kondo liquid
regime, and the hidden-order phase. The normal state is characterized by an
anisotropic behavior between the ab plane and c axis responses. The ab plane
optical conductivity is strongly influenced by the formation of the coherent
Kondo liquid: a sharp Drude peak develops and a hybridization gap at 12 meV
leads to a spectral weight transfer to mid-infrared energies. The c axis
conductivity has a different behavior: the Drude peak already exists at 300 K
and no particular anomaly or gap signature appears in the coherent Kondo liquid
regime. When entering the hidden-order state, both polarizations see a dramatic
decrease in the Drude spectral weight and scattering rate, compatible with a
loss of about 50 % of the carriers at the Fermi level. At the same time a
density-wave like gap appears along both polarizations at about 6.5 meV at 5 K.
This gap closes respecting a mean field thermal evolution in the ab plane.
Along the c axis it remains roughly constant and it "fills up" rather than
closing.Comment: 10 pages, 7 figure
Coexistence of orbital and quantum critical magnetoresistance in FeSeS
The recent discovery of a non-magnetic nematic quantum critical point (QCP)
in the iron chalcogenide family FeSeS has raised the prospect of
investigating, in isolation, the role of nematicity on the electronic
properties of correlated metals. Here we report a detailed study of the normal
state transverse magnetoresistance (MR) in FeSeS for a series of
S concentrations spanning the nematic QCP. For all temperatures and
\textit{x}-values studied, the MR can be decomposed into two distinct
components: one that varies quadratically in magnetic field strength
and one that follows precisely the quadrature scaling form
recently reported in metals at or close to a QCP and characterized by a
\textit{H}-linear MR over an extended field range. The two components evolve
systematically with both temperature and S-substitution in a manner that is
determined by their proximity to the nematic QCP. This study thus reveals
unambiguously the coexistence of two independent charge sectors in a quantum
critical system. Moreover, the quantum critical component of the MR is found to
be less sensitive to disorder than the quadratic (orbital) MR, suggesting that
detection of the latter in previous MR studies of metals near a QCP may have
been obscured.Comment: 19 pages (including Supplemental Material), 12 figure
The Effects of Stacking on the Configurations and Elasticity of Single Stranded Nucleic Acids
Stacking interactions in single stranded nucleic acids give rise to
configurations of an annealed rod-coil multiblock copolymer. Theoretical
analysis identifies the resulting signatures for long homopolynucleotides: A
non monotonous dependence of size on temperature, corresponding effects on
cyclization and a plateau in the extension force law. Explicit numerical
results for poly(dA) and poly(rU) are presented.Comment: 4 pages and 2 figures. Accepted in Phys. Rev. E Rapid Com
Fluctuation-dissipation relations in the activated regime of simple strong-glass models
We study the out-of-equilibrium fluctuation-dissipation (FD) relations in the
low temperature, finite time, physical aging regime of two simple models with
strong glass behaviour, the Fredrickson-Andersen model and the square-plaquette
interaction model. We explicitly show the existence of unique, waiting-time
independent dynamical FD relations. While in the Fredrickson-Andersen model the
FD theorem is obeyed at all times, the plaquette model displays piecewise
linear FD relations, similar to what is found in disordered mean-field models
and in simulations of supercooled liquids, and despite the fact that its static
properties are trivial. We discuss the wider implications of these results.Comment: 4 pages, 3 figure
Simple strong glass forming models: mean-field solution with activation
We introduce simple models, inspired by previous models for froths and
covalent glasses, with trivial equilibrium properties but dynamical behaviour
characteristic of strong glass forming systems. These models are also a
generalization of backgammon or urn models to a non--constant number of
particles, where entropic barriers are replaced by energy barriers, allowing
for the existence of activated processes. We formulate a mean--field version of
the models, which keeps most of the features of the finite dimensional ones,
and solve analytically the out--of--equilibrium dynamics in the low temperature
regime where activation plays an essential role.Comment: 18 pages, 9 figure
Statistical Mechanics of Soft Margin Classifiers
We study the typical learning properties of the recently introduced Soft
Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the
tools of Statistical Mechanics. We derive analytically the behaviour of the
learning curves in the regime of very large training sets. We obtain
exponential and power laws for the decay of the generalization error towards
the asymptotic value, depending on the task and on general characteristics of
the distribution of stabilities of the patterns to be learned. The optimal
learning curves of the SMCs, which give the minimal generalization error, are
obtained by tuning the coefficient controlling the trade-off between the error
and the regularization terms in the cost function. If the task is realizable by
the SMC, the optimal performance is better than that of a hard margin Support
Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review
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