Three-dimensional x−yx-y model with the Chern-Simons term

We investigate the influence of the Chern-Simons term coupled to the three-dimensional $x-y$ model. This term endows vortices with an internal angular momentum and thus gives them arbitrary statistics. The Chern-Simons term for the $x-y$ model takes an integer value which can be written as a sum over all vortex lines of the product of the vortex charge and the winding number of the internal phase angle along that vortex line. We have used the Monte-Carlo method to study the three-dimensional $x-y$ model with the Chern-Simons term. Our findings suggest that this model belongs to the $x-y$ universality class with the critical temperature growing with increasing internal angular momentum.Comment: 15 pages, uuencoded postscript fil

Boundary effects in superfluid films

We have studied the superfluid density and the specific heat of the XY model on lattices L x L x H with L >> H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In the H-direction we applied staggered boundary conditions so that the order parameter on the top and bottom layers is zero, whereas periodic boundary conditions were applied in the L-directions. We find that the system exhibits a Kosterlitz-Thouless phase transition at the H-dependent temperature T_{c}^{2D} below the critical temperature T_{\lambda} of the bulk system. However, right at the critical temperature the ratio of the areal superfluid density to the critical temperature is H-dependent in the range of film thicknesses considered here. We do not find satisfactory finite-size scaling of the superfluid density with respect to H for the sizes of H studied. However, our numerical results can be collapsed onto a single curve by introducing an effective thickness H_{eff} = H + D (where D is a constant) into the corresponding scaling relations. We argue that the effective thickness depends on the type of boundary conditions. Scaling of the specific heat does not require an effective thickness (within error bars) and we find good agreement between the scaling function f_{1} calculated from our Monte Carlo results, f_{1} calculated by renormalization group methods, and the experimentally determined function f_1.Comment: 37 pages,15 postscript figure

Scaling of the specific heat of superfluids confined in pores

We investigate the scaling properties of the specific heat of the XY model on lattices H x H x L with L >> H (i.e. in a bar-like geometry) with respect to the thickness H of the bar, using the Cluster Monte Carlo method. We study the effect of the geometry and boundary conditions on the shape of the universal scaling function of the specific heat by comparing the scaling functions obtained for cubic, film, and bar-like geometry. In the presence of physical boundary conditions applied along the sides of the bars we find good agreement between our Monte Carlo results and the most recent experimental data for superfluid helium confined in pores.Comment: 10 pages, 4 figures, Revte

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

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

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

The specific heat of superfluids near the transition temperature

The specific heat of the $x-y$ model is studied on cubic lattices of sizes $L \times L \times L$ and 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. Periodic boundary conditions were applied in all directions. In the cubic case we obtained the ratio of the critical exponents $\alpha/\nu$ from the size dependence of the energy density at the critical temperature $T_{\lambda}$. 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

Boundary effects in superfluid films

We have studied the superfluid density and the specific heat of the x − y model on lattices L × L × H with L ≫ H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In the H-direction we applied staggered boundary conditions so that the order parameter on the top and bottom layers is zero, whereas periodic boundary conditions were applied in the L-directions. We find that the system exhibits a Kosterlitz-Thouless phase transition at the H-dependent temperature T 2D c below the critical temperature Tλ of the bulk system. However, right at the critical temperature the ratio of the areal superfluid density to the critical temperature is H-dependent in the range of film thicknesses considered here. We do not find satisfactory finite-size scaling of the superfluid density with respect to H for the sizes of H studied. However, our numerical results can be collapsed onto a single curve by introducing an effective thickness Heff = H +D (where D is a constant) into the corresponding scaling relations. We argue that the effective thickness depends on the type of boundary conditions. Scaling of the specific heat does not require an effective thickness (within error bars) and we find good agreement between the scaling function f1 calculated from our Monte Carlo results, f1 calculated by renormalization group methods, and 1 the experimentally determined function f1

Scaling of the Specific Heat of Superfluids Confined in Pores

this paper, we report results of our simulations of the XY model in a bar-like geometry, namely on lattices H \Theta H \Theta