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

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

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

The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-

We simulate the improved three-dimensional two-component phi^4 model on the simple cubic lattice in the low and the high temperature phase for reduced temperatures down to |T-T_c|/T_c \approx 0.0017 on lattices of a size up to 350^3. Our new results for the internal energy and the specific heat are combined with the accurate estimates of beta_c and data for the internal energy and the specific heat at \beta_c recently obtained in cond-mat/0605083. We find R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5), where alpha is the critical exponent of the specific heat and A_{\pm} is the amplitude of the specific heat in the high and the low temperature phase, respectively.Comment: 14 pages, 4 figure

Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4

We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size scaling method. We find that there exists a finite value of the coupling lambda^*, for both values of N, where leading corrections to scaling vanish. As a first application, we compute the critical exponents nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for N=4.Comment: 21 pages, 2 figure

The two dimensional XY model at the transition temperature: A high precision Monte Carlo study

We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature.Comment: Monte Carlo results for xi/L in table 1 and 2 corrected. Due to a programming error,these numbers were wrong by about a factor 1+1/L^2. Correspondingly the fits with L_min=64 and 128 given in table 5 and 6 are changed by little.The central results of the paper are not affected. Wrong sign in eq.(52) corrected. Appendix extende

Effective string picture for confinement at finite temperature: theoretical predictions and high precision numerical results

The effective string picture of confinement is used to derive theoretical predictions for the interquark potential at finite temperature. At short distances, the leading string correction to the linear confining potential between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a Nambu--Goto effective string action, and work out subleading contributions in an analytical way. We discuss the contribution given by a possible ``boundary term'' in the effective action, comparing these predictions with results from simulations of lattice $Z_2$ gauge theory in three dimensions, obtained with an algorithm which exploits the duality of the $Z_2$ gauge model with the Ising spin model.Comment: Lattice2003(nonzero), 3 pages, 2 figure

The uniformly frustrated two-dimensional XY model in the limit of weak frustration

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behaviour of the XY model for T <= T_{KT}, where T_{KT} is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behaviour of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.Comment: 12 page