arXiv subjects
Publications and source records attributed to N. Schultka.
We study numerically the influence of the substrate (boundary conditions) on the finite--size scaling properties of the superfluid density $ρ_s$ in superfluid films of thickness $H$ within the XY model employing the Monte Carlo method. Our results suggest that the jump $ρ_s H/T_c$ at the Kosterlitz--Thouless transition temperature $T_c$ depends on the boundary conditions.
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.
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 $α/ν$ from the size dependence of the energy density at the critical temperature $T_λ$. 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.
We have studied the superfluid density $ρ_{s}$ on various size-lattices in the geometry $L \times L \times H$ by numerical simulation of the $x-y$ model using the Cluster Monte Carlo method. Applying the Kosterlitz-Thouless-Nelson renormalization group equations for the superfluid density we have been able to extrapolate to the $L \to \infty$ limit for a given value of $H$. In the superfluid phase we find that the superfluid density faithfully obeys the expected scaling law with $H$, using the experimental value for the critical exponent $ν=0.6705$. For the sizes of film thickness studied here the critical temperature $T_{c}$ and the coefficient $b$ entering the equation $T/(ρ_{s} H) \propto 1-b(1-T/T_{c})^{1/2}$ are in agreement with the expected $H$-dependence deduced from general scaling ideas.
The topological vacuum structure of the two-dimensional $~CP^{n-1}~$ model for $~n = 3,5,7~$ is studied on the lattice. In particular we investigate the small-volume limit on the torus as well as on the sphere and compare with continuum results. For $~n \ge 5~$ , where lattice artifacts should be suppressed, the topological susceptibility shows unexpectedly strong deviations from asymptotic scaling. On the other hand there is an indication for a convergence to values obtained analytically within the limit $~n \rightarrow \infty~$ .