A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios

We simulate lattice models in the three-dimensional XY universality class in the low and the high temperature phase. This allows us to compute a number of universal amplitude ratios with unprecedented precision: R_{\Upsilon}=0.411(2), R_B=2.83(1), R_{\xi}^+=0.3562(10) and R_{\xi}^-=0.850(5). These results can be compared with those obtained from other theoretical methods, such as field theoretic methods or the high temperature series expansion and also with experimental results for the lambda-transition of $^4$He. In addition to the XY model, we study the three-dimensional two-component $\phi^4$ model on the simple cubic lattice. The parameter of the $\phi^4$ model is chosen such that leading corrections to scaling are small.Comment: 28 pages 5 figure

Speeding up the HMC: QCD with Clover-Improved Wilson Fermions

We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavor QCD with clover-improvement. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.Comment: 3 pages, lattice2002, algorithms, DESY Report-no correcte

Rough Interfaces Beyond the Gaussian Approximation

We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).Comment: Contribution to LATTICE 94. 3 pages, PostScript fil

Thermodynamic Casimir effect: Universality and Corrections to Scaling

We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. We focus on the effect of corrections to scaling and probe numerically the universality of our results. In particular we check our hypothesis that corrections are well described by an effective thickness L_{0,eff}=L_0+c (L_0+L_s)^{1-\omega} +L_s, where c and L_s are system specific parameters and \omega\approx 0.8 is the exponent of the leading bulk correction. We simulate the improved Blume-Capel model and the Ising model on the simple cubic lattice. First we analyse the behaviour of various quantities at the critical point. Taking into account corrections \propto L_0^{-\omega} in the case of the Ising model, we find good consistency of results obtained from these two different models. In particular we get from the analysis of our data for the Ising model for the difference of Casimir amplitudes \Delta_{+-}-\Delta_{++}=3.200(5), which nicely compares with \Delta_{+-}-\Delta_{++}=3.208(5) obtained by studying the improved Blume-Capel model. Next we study the behaviour of the thermodynamic Casimir force for large values of the scaling variable x=t [L_0/\xi_0]. This behaviour can be obtained up to an overall amplitude by expressing the partition function of the film in terms of eigenvalues and eigenstates of the transfermatrix and boundary states. Here we show how this overall amplitude can be computed with high accuracy. Finally we discuss our results for the scaling functions \theta_{+-} and \theta_{++} of the thermodynamic Casimir force for the whole range of the scaling variable. We conclude that our numerical results are in accordance with universality. Corrections to scaling are well approximated by an effective thickness.Comment: 35 pages, 5 figures, various typos correcte