58,723 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
Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
We study the finite-size scaling properties of the Ising model on the Moebius
strip and the Klein bottle. The results are compared with those of the Ising
model under different boundary conditions, that is, the free, cylindrical, and
toroidal boundary conditions. The difference in the magnetization distribution
function for various boundary conditions is discussed in terms of the
number of the percolating clusters and the cluster size. We also find
interesting aspect-ratio dependence of the value of the Binder parameter at
for various boundary conditions. We discuss the relation to the
finite-size correction calculations for the dimer statistics.Comment: 4 pages including 5 eps figures, RevTex, to appear in Phys. Rev. Let
Can Hall drag be observed in Coulomb coupled quantum wells in a magnetic field?
We study the transresistivity \tensor\rho_{21} (or equivalently, the drag
rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular
magnetic field, using semi-classical transport theory. Elementary arguments
seem to preclude any possibility of observation of ``Hall drag'' (i.e., a
non-zero off-diagonal component in \tensor\rho_{21}). We show that these
arguments are specious, and in fact Hall drag can be observed at sufficiently
high temperatures when the {\sl intra}layer transport time has
significant energy-dependence around the Fermi energy . The
ratio of the Hall to longitudinal transresistivities goes as , where
is the temperature, is the magnetic field, and .Comment: LaTeX, 13 pages, 2 figures (to be published in Physica Scripta, Proc.
of the 17th Nordic Semiconductor Conference
Techniques for Accurate Parallax Measurements for 6.7-GHz Methanol Masers
The BeSSeL Survey is mapping the spiral structure of the Milky Way by
measuring trigonometric parallaxes of hundreds of maser sources associated with
high-mass star formation. While parallax techniques for water masers at high
frequency (22 GHz) have been well documented, recent observations of methanol
masers at lower frequency (6.7 GHz) have revealed astrometric issues associated
with signal propagation through the ionosphere that could significantly limit
parallax accuracy. These problems displayed as a "parallax gradient" on the sky
when measured against different background quasars. We present an analysis
method in which we generate position data relative to an "artificial quasar" at
the target maser position at each epoch. Fitting parallax to these data can
significantly mitigate the problems and improve parallax accuracy
Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime
A recent theory has provided a possible explanation for the ``non-universal
scaling'' of the low-temperature conductance (and conductivity) peak-heights of
two-dimensional electron systems in the integer and fractional quantum Hall
regimes. This explanation is based on the hypothesis that samples which show
this behavior contain density inhomogeneities. Theory then relates the
non-universal conductance peak-heights to the ``number of alternating
percolation clusters'' of a continuum percolation model defined on the
spatially-varying local carrier density. We discuss the statistical properties
of the number of alternating percolation clusters for Corbino disc samples
characterized by random density fluctuations which have a correlation length
small compared to the sample size. This allows a determination of the
statistical properties of the low-temperature conductance peak-heights of such
samples. We focus on a range of filling fraction at the center of the plateau
transition for which the percolation model may be considered to be critical. We
appeal to conformal invariance of critical percolation and argue that the
properties of interest are directly related to the corresponding quantities
calculated numerically for bond-percolation on a cylinder. Our results allow a
lower bound to be placed on the non-universal conductance peak-heights, and we
compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and
multicol.sty. The revised version contains some additional discussion of the
theory and slightly improved numerical result
Random-cluster multi-histogram sampling for the q-state Potts model
Using the random-cluster representation of the -state Potts models we
consider the pooling of data from cluster-update Monte Carlo simulations for
different thermal couplings and number of states per spin . Proper
combination of histograms allows for the evaluation of thermal averages in a
broad range of and values, including non-integer values of . Due to
restrictions in the sampling process proper normalization of the combined
histogram data is non-trivial. We discuss the different possibilities and
analyze their respective ranges of applicability.Comment: 12 pages, 9 figures, RevTeX
Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :
Let f, U and C represent, respectively, the free energy, the internal energy
and the specific heat of the critical Ising model on the square M x N lattice
with periodic boundary conditions. We find that N f and U are well-defined odd
function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1))
finite-size corrections amplitudes for the internal energy and the specific
heat are constant. The free energy and the internal energy at the critical
point are calculated asymtotically up to N^(-5) order, and the specific heat up
to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February
200
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