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 $p(m)$ 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 $T=T_c$ 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 $\tau$ has significant energy-dependence around the Fermi energy $\varepsilon_F$. The ratio of the Hall to longitudinal transresistivities goes as $T^2 B s$, where $T$ is the temperature, $B$ is the magnetic field, and $s = [\partial\tau/ \partial\varepsilon] (\varepsilon_F)$.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 $q$-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings $K$ and number of states per spin $q$. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of $K$ and $q$ values, including non-integer values of $q$. 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