71,345 research outputs found
Geometry, thermodynamics, and finite-size corrections in the critical Potts model
We establish an intriguing connection between geometry and thermodynamics in
the critical q-state Potts model on two-dimensional lattices, using the q-state
bond-correlated percolation model (QBCPM) representation. We find that the
number of clusters of the QBCPM has an energy-like singularity for q different
from 1, which is reached and supported by exact results, numerical simulation,
and scaling arguments. We also establish that the finite-size correction to the
number of bonds, has no constant term and explains the divergence of related
quantities as q --> 4, the multicritical point. Similar analyses are applicable
to a variety of other systems.Comment: 12 pages, 6 figure
Notes on two-parameter quantum groups, (I)
A simpler definition for a class of two-parameter quantum groups associated
to semisimple Lie algebras is given in terms of Euler form. Their positive
parts turn out to be 2-cocycle deformations of each other under some
conditions. An operator realization of the positive part is given.Comment: 11 page
Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters
Percolation models with multiple percolating clusters have attracted much
attention in recent years. Here we use Monte Carlo simulations to study bond
percolation on planar random lattices, duals of random
lattices, and square lattices with free and periodic boundary conditions, in
vertical and horizontal directions, respectively, and with various aspect ratio
. We calculate the probability for the appearance of
percolating clusters, the percolating probabilities, , the average
fraction of lattice bonds (sites) in the percolating clusters,
(), and the probability distribution function for the fraction
of lattice bonds (sites), in percolating clusters of subgraphs with
percolating clusters, (). Using a small number of
nonuniversal metric factors, we find that , ,
(), and () for random lattices, duals
of random lattices, and square lattices have the same universal finite-size
scaling functions. We also find that nonuniversal metric factors are
independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure
On the non-Gaussianity from Recombination
The non-linear effects operating at the recombination epoch generate a
non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant
because it represents a major part of the second-order radiation transfer
function which must be determined in order to have a complete control of both
the primordial and non-primordial part of non-Gaussianity in the CMB
anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB
arising from the recombination epoch which shows up mainly in the equilateral
configuration. We find that it causes a contamination to the possible
measurement of the equilateral primordial bispectrum shifting the minimum
detectable value of the non-Gaussian parameter f^equil_NL by Delta f^equil_NL=
O(10) for an experiment like Planck.Comment: LaTeX file; 11 pages. v2: Typos corrected; references added; comments
about the effective non-linearity parameter added in Sec. IV; comments added
in the conclusions of Sec. IV. v3: References added; some clarifications
added as footnotes 4 and 6, and in Sec. 3. Matches version accepted for
publication in JCA
Contact and sum-rules in a near-uniform Fermi gas at unitarity
We present an experimental study of the high-energy excitation spectra of
unitary Fermi gases. Using focussed beam Bragg spectroscopy, we locally probe
atoms in the central region of a harmonically trapped cloud where the density
is nearly uniform, enabling measurements of the dynamic structure factor for a
range of temperatures both below and above the superfluid transition. Applying
sum-rules to the measured Bragg spectra, we resolve the characteristic
behaviour of the universal contact parameter, , across the superfluid
transition. We also employ a recent theoretical result for the kinetic
(second-moment) sum-rule to obtain the internal energy of gases at unitarity.Comment: 5 pages, 4 figure
The effect of the thermal conductivity of the substrate on droplet evaporation
The evaporation of liquid droplets is of fundamental importance to industry, with a vast number of applications including ink-jet printing, spray cooling and DNA mapping, and has been the subject of considerable theoretical and experimental research in recent years. Significant recent papers include those by Deegan [1], Deegan et al. [2], Hu and Larson [3], Poulard et al. [4], Sultan et al. [5], and Shahidzadeh-Bonn et al. [6]
Evidence for electron-phonon interaction in FeMSb (M=Co, Cr) single crystals
We have measured polarized Raman scattering spectra of the
FeCoSb and FeCrSb (00.5)
single crystals in the temperature range between 15 K and 300 K. The highest
energy symmetry mode shows significant line asymmetry due to phonon
mode coupling width electronic background. The coupling constant achieves the
highest value at about 40 K and after that it remains temperature independent.
Origin of additional mode broadening is pure anharmonic. Below 40 K the
coupling is drastically reduced, in agreement with transport properties
measurements. Alloying of FeSb with Co and Cr produces the B mode
narrowing, i.e. weakening of the electron-phonon interaction. In the case of
A symmetry modes we have found a significant mode mixing
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