45 research outputs found
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
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
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 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 is extremely unlikely in this model.Comment: 4 pages, 3 Postscript figures, to appear in Phys. Rev. B Jan. 1997 as
a Brief Repor
Classical Phase Fluctuations in High Temperature Superconductors
Phase fluctuations of the superconducting order parameter play a larger role
in the cuprates than in conventional BCS superconductors because of the low
superfluid density of a doped insulator. In this paper, we analyze an XY model
of classical phase fluctuations in the high temperature superconductors using a
low-temperature expansion and Monte Carlo simulations. In agreement with
experiment, the value of the superfluid density at temperature T=0 is a quite
robust predictor of Tc, and the evolution of the superfluid density with T,
including its T-linear behavior at low temperature, is insensitive to
microscopic details.Comment: 4 pages, 1 figur
Thermal excitations of frustated XY spins in two dimensions
We present a new variational approach to the study of phase transitions in
frustrated 2D XY models. In the spirit of Villain's approach for the
ferromagnetic case we divide thermal excitations into a low temperature long
wavelength part (LW) and a high temperature short wavelength part (SW). In the
present work we mainly deal with LW excitations and we explicitly consider the
cases of the fully frustrated triangular (FFTXY) and square ( FFSQXY) XY
models. The novel aspect of our method is that it preserves the coupling
between phase (spin angles) and chiral degrees of freedom. LW fluctuations
consist of coupled phase and chiral excitations. As a result, we find that for
frustrated systems the effective interactions between phase variables is long
range and oscillatory in contrast to the unfrustrated problem. Using Monte
Carlo (MC) simulations we show that our analytical calculations produce
accurate results at all temperature ; this is seen at low in the spin
wave stiffness constant and in the staggered chirality; this is also the case
near : transitions are driven by the SW part associated with domain walls
and vortices, but the coupling between phase and chiral variables is still
relevant in the critical region. In that regime our analytical results yield
the correct dependence for bare couplings (given by the LW fluctuations)
such as the Coulomb gas temperature of the frustrated XY models . In
particular we find that tracks chiral rather than phase fluctuations.
Our results provides support for a single phase transition scenario in the
FFTXY and FFSQXY models.Comment: 32 pages, RevTex, 11 eps figures available upon request, article to
appear in Phys. Rev.
The specific heat of superfluids near the transition temperature
The specific heat of the model is studied on cubic lattices of sizes and on lattices with (i.e.
on lattices representing a film geometry) using the Cluster Monte Carlo method.
Periodic boundary conditions were applied in all directions. In the cubic case
we obtained the ratio of the critical exponents from the size
dependence of the energy density at the critical temperature .
Using finite--size scaling theory, we find that while for both geometries our
results scale to universal functions, these functions differ for the different
geometries. We compare our findings to experimental results and results of
renormalization group calculations.Comment: self-unpacking uuencoded PostScript file (for instructions see the
beginning of the file), 18 pages
Duality and Universality for the Chern-Simons bosons
By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg
theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the
Chern-Simons gauge field, we investigate phase transitions of Chern-Simons
bosons in the limit of strong coupling. We construct algebraically exact
duality and flux attachment transformations of the lattice theories,
corresponding to analogous transformations in the continuum limit. These
transformations are used to convert the model with arbitrary fractional
Chern-Simons coefficient to a model with either zero or one.
Depending on this final value of , the phase transition in the original
model is either in the universality class of the 3D x-y model or a
``fermionic'' universality class, unless the irrelevant corrections of cubic
and higher power in momenta render the transition of the first order.Comment: 14 two-column pages, revtex 3.0, multicol and epsf.sty (optional),
one PostScript figure, Submitted to Phys. Rev. B The changes intended to
simplify the arguments and eliminate logical gaps. We also show how the
filling factor is changed by the duality transformatio