60 research outputs found
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 in
superfluid films of thickness within the XY model employing the Monte Carlo
method. Our results suggest that the jump at the
Kosterlitz--Thouless transition temperature depends on the boundary
conditions.Comment: 2 pages, 1 Latex file, 1 postscript figure, 2 style file
Scaling of the specific heat in superfluid films
We study the specific heat of the model on lattices with (i.e. on lattices representing a film geometry) using the
Cluster Monte--Carlo method. In the --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
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
Scaling of the superfluid density in superfluid films
We study scaling of the superfluid density with respect to the film thickness
by simulating the model on films of size ()
using the cluster Monte Carlo. While periodic boundary conditions where used in
the planar () 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 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 .Comment: 4 pages, one postscript file replaced by one Latex file and 5
postscript figure
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 with . We have applied open boundary conditions on the bar
sides (the confined directions of length ) 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
in the time step . 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
Critical behavior of the planar magnet model in three dimensions
We use a hybrid Monte Carlo algorithm in which a single-cluster update is
combined with the over-relaxation and Metropolis spin re-orientation algorithm.
Periodic boundary conditions were applied in all directions. We have calculated
the fourth-order cumulant in finite size lattices using the single-histogram
re-weighting method. Using finite-size scaling theory, we obtained the critical
temperature which is very different from that of the usual XY model. At the
critical temperature, we calculated the susceptibility and the magnetization on
lattices of size up to . Using finite-size scaling theory we accurately
determine the critical exponents of the model and find that =0.670(7),
=1.9696(37), and =0.515(2). Thus, we conclude that the
model belongs to the same universality class with the XY model, as expected.Comment: 11 pages, 5 figure
Lattice knot theory and quantum gravity in the loop representation
We present an implementation of the loop representation of quantum gravity on
a square lattice. Instead of starting from a classical lattice theory,
quantizing and introducing loops, we proceed backwards, setting up constraints
in the lattice loop representation and showing that they have appropriate
(singular) continuum limits and algebras. The diffeomorphism constraint
reproduces the classical algebra in the continuum and has as solutions lattice
analogues of usual knot invariants. We discuss some of the invariants stemming
from Chern--Simons theory in the lattice context, including the issue of
framing. We also present a regularization of the Hamiltonian constraint. We
show that two knot invariants from Chern--Simons theory are annihilated by the
Hamiltonian constraint through the use of their skein relations, including
intersections. We also discuss the issue of intersections with kinks. This
paper is the first step towards setting up the loop representation in a
rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi
High precision Monte Carlo study of the 3D XY-universality class
We present a Monte Carlo study of the two-component model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
and , 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
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, , 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
Finite-Size Scaling in Two-Dimensional Superfluids
Using the 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 up to . This technique
allows us to approach temperatures close to the critical point, and by studying
a wide range of 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
Percolation properties of the 2D Heisenberg model
We analyze the percolation properties of certain clusters defined on
configurations of the 2--dimensional Heisenberg model. We find that, given any
direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form
a percolating cluster. This result gives indications of how the model can avoid
a previously conjectured Kosterlitz-Thouless phase transition at finite
temperature T.Comment: 4 pages, 3 eps figures. Revised version (more clear abstract, some
new references
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