Boundary effects on the scaling of the superfluid density

We study numerically the influence of the substrate (boundary conditions) on the finite--size scaling properties of the superfluid density $\rho_s$ in superfluid films of thickness $H$ within the XY model employing the Monte Carlo method. Our results suggest that the jump $\rho_s H/T_c$ at the Kosterlitz--Thouless transition temperature $T_c$ depends on the boundary conditions.Comment: 2 pages, 1 Latex file, 1 postscript figure, 2 style file

Scaling of the superfluid density in superfluid films

We study scaling of the superfluid density with respect to the film thickness by simulating the $x-y$ model on films of size $L \times L \times H$ ($L >> H$) using the cluster Monte Carlo. While periodic boundary conditions where used in the planar ($L$) directions, Dirichlet boundary conditions where used along the film thickness. We find that our results can be scaled on a universal curve by introducing an effective thickness. In the limit of large $H$ our scaling relations reduce to the conventional scaling forms. Using the same idea we find scaling in the experimental results using the same value of $\nu = 0.6705$.Comment: 4 pages, one postscript file replaced by one Latex file and 5 postscript figure

Ein fruktifizierender Sproß von <i>Asolanus camptotaenia</i> Wood aus dem Westfal D Nordwestdeutschlands

Erstmalig wird der fruktifizierende Sproß von Asolanus camptotaenia beschrieben. Bei den nachgewiesenen fertilen Organen handelt es sich um Megasporangien, Microsporangien sind noch nicht gefunden worden. Der Bau des fertilen Sprosses sowie die Organisation der Sporophylle belegen die isolierte Stellung der Gattung Asolanus innerhalb der Lepidophyta. A megasporangia bearing axis of Asolanus camptotaenia Wood from the Westphalian D of Northwestern Germany A fertil impression axis of Asolanus camptotaenia from Westfalian D strata is described. While some megasporangia are found, microsporangia are not yet established. The type specimen is not very well characterized by Wood 1860, but all differences described til now would be caused by preservation. The diagonal striation from cushion to cushion also is only a special mode of preservation and useless for taxonomic purposes. Well sculptered Asolanus-axis from the Stephanian belong to the genus Lepidodendron or possibly to a new not yet described genus. Lepidostrobus foliaceus and Lepidophyllum truncatus mentioned by Lesquereux 1880 as well as Gymnostrobus salisbury described by Bureau 1914 may belong to A. camptotaenia. The organisation of the fertil axis from the Piesberg demonstrates an isolated position of this genus within the lepidophytes not so far from Pinakodendron and relatives. doi:10.1002/mmng.19980010110</a

Scaling of the specific heat in superfluid films

We study the specific heat of the $x-y$ model on lattices $L \times L \times H$ with $L \gg H$ (i.e. on lattices representing a film geometry) using the Cluster Monte--Carlo method. In the $H$--direction we apply Dirichlet boundary conditions so that the order parameter in the top and bottom layers is zero. We find that our results for the specific heat of various thickness size $H$ collapse on the same universal scaling function. The extracted scaling function of the specific heat is in good agreement with the experimentally determined universal scaling function using no free parameters.Comment: 4 pages, uuencoded compressed PostScrip

Cuticles of <i>Karinopteris beneckei</i> (Potonié ex Huth) Boersma emend., a mariopterid seed fern from the Upper Carboniferous of Lower Silesia (Poland)

Cuticles of Karinopteris beneckei are described from the upper Westphalian A of Lower Silesia (Poland). The diagnosis for Karinopteris beneckei (Potonié ex Huth, 1912) Boersma, 1972 is emended based on additional macroscopic observations and data on the epidermal anatomy. Karinopteris beneckei closely resembles K. acuta with regard to macromorphology, but a number of features indicate that the two taxa are not conspecific. Some comments are offered on the paleobiological and paleoecological implications of particular features observed from K. beneckei (e.g., climber hooks confined to distal frond portions, large emergences, and minute stomata) where they are considered relative to adaptations of the plant to special mechanical, ecological, and physiological requirements. Aus dem oberen Westfal A von Niederschlesien (Polen) werden erstmalig die Kutikulen von Karinopteris beneckei beschrieben. Auf der Basis zusätzlicher Beobachtungen zur Makromorphologie und unter Einbeziehung der epidermalen Anatomie wird die Diagnose für Karinopteris beneckei (Potonié ex Huth, 1912) Boersma, 1972 emendiert. Karinopteris beneckei und K. acuta sind makromorphologisch sehr ähnlich; einige Unterschiede unterstützen allerdings die taxonomische Eigenständigkeit beider Formen. Einige Merkmale von K. beneckei (z.B. das ausschließliche Vorkommen von Kletterhaken im distalen Teil der Wedel, ein besonderer Typ von Emergenzen, bemerkenswert kleine Stomata) werden in Hinsicht auf ihre Signifikanz ín Paläobiologie und -ökologie diskutiert; vermutlich stellen sie Adaptationen der Pflanze an bestimmte Habitatkonditionen dar. doi:10.1002/mmng.20020050120</a

Scaling of thermal conductivity of helium confined in pores

We have studied the thermal conductivity of confined superfluids on a bar-like geometry. We use the planar magnet lattice model on a lattice $H\times H\times L$ with $L \gg H$. We have applied open boundary conditions on the bar sides (the confined directions of length $H$) and periodic along the long direction. We have adopted a hybrid Monte Carlo algorithm to efficiently deal with the critical slowing down and in order to solve the dynamical equations of motion we use a discretization technique which introduces errors only $O((\delta t)^6)$ in the time step $\delta t$. Our results demonstrate the validity of scaling using known values of the critical exponents and we obtained the scaling function of the thermal resistivity. We find that our results for the thermal resistivity scaling function are in very good agreement with the available experimental results for pores using the tempComment: 5 two-column pages, 3 figures, Revtex

Nematic phase of the two-dimensional electron gas in a magnetic field

The two dimensional electron gas (2DEG) in moderate magnetic fields in ultra-clean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible, anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature, $T_c \sim 65 mK$, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.Comment: 4 pages, 3 figure

High precision Monte Carlo study of the 3D XY-universality class

We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics simulations using finite size scaling techniques yield $\nu=0.6723(3)[8]$ and $\eta=0.0381(2)[2]$, where the statistical and systematical errors are given in the first and second bracket, respectively. These results are more precise than any previous theoretical estimate of the critical exponents for the 3D XY universality class.Comment: 13 page

Finite-Size Scaling in Two-Dimensional Superfluids

Using the $x-y$ model and a non-local updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two dimensional superfluid on large-size square lattices $L \times L$ up to $400\times 400$. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of $L$ values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson Renormalization Group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.Comment: 13 pages, postscript fil

Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to the low temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low temperature expansion of the finite-size scaling function and for the low temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature $T > 0$ is extremely unlikely in this model.Comment: 4 pages, 3 Postscript figures, to appear in Phys. Rev. B Jan. 1997 as a Brief Repor