Graphical representations and cluster algorithms for critical points with fields

A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical representation. Results from numerical simulations of the Ising model in a staggered field are presented. The dynamic exponent for the algorithm is measured to be less than 0.5.Comment: Revtex, 12 pages with 2 figure

Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo

We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to overcome critial slowing down for a given model. Our method is introduced in the context of spin models. A multigrid Monte Carlo procedure for nonabelian lattice gauge theory is described, and its kinematics is analyzed in detail.Comment: 7 pages, no figures, (talk at LATTICE 92 in Amsterdam

Universal amplitudes in the FSS of three-dimensional spin models

In a MC study using a cluster update algorithm we investigate the finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical O(n) symmetric spin models on a column geometry. For all considered models we find strong evidence for a linear relation between FSS amplitudes and scaling dimensions when applying antiperiodic instead of periodic boundary conditions across the torus. The considered type of scaling relation can be proven analytically for systems on two-dimensional strips with periodic bc using conformal field theoryComment: 4 pages, RevTex, uses amsfonts.sty, 3 Figure

Kinematics of Multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.Comment: 28 pages, 8 ps-figures, DESY 92-09

The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity

A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice. Just as the connectivity of the original lattice is meant to be a lattice representation of the metric, the block links are determined in such a way that the connectivity of the block lattice represents a block metric. As an illustration, this approach is applied to the Ising model coupled to two-dimensional quantum gravity. The correct critical coupling is reproduced, but the critical exponent is obscured by unusually large finite size effects.Comment: 10 page

Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetization is obtained through finite-size scaling, using a corner transfer matrix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen model. Through a conformal mapping of the system onto a strip, the gap-exponent relation is shown to remain valid for such an aperiodic defect.Comment: 12 pages, TeX file + 4 figures, epsf neede

Cluster algorithms

Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster and single--cluster methods, and of the standard and improved estimators are compared. (Lecture given at the summer school on `Advances in Computer Simulations', Budapest, July 1996.)Comment: 17 pages, Late

Monte Carlo simulation of ice models

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.Comment: 32 pages including 15 postscript figures, typeset in LaTeX2e using the Elsevier macro package elsart.cl

A Quantitative Comparison of SMC, LMC, and Milky Way UV to NIR Extinction Curves

We present an exhaustive, quantitative comparison of all of the known extinction curves in the Small and Large Magellanic Clouds (SMC and LMC) with our understanding of the general behavior of Milky Way extinction curves. The R_V dependent CCM relationship and the sample of extinction curves used to derive this relationship is used to describe the general behavior of Milky Way extinction curves. The ultraviolet portion of the SMC and LMC extinction curves are derived from archival IUE data, except for one new SMC extinction curve which was measured using HST/STIS observations. The optical extinction curves are derived from new (for the SMC) and literature UBVRI photometry (for the LMC). The near-infrared extinction curves are calculated mainly from 2MASS photometry supplemented with DENIS and new JHK photometry. For each extinction curve, we give R_V = A(V)/E(B-V) and N(HI) values which probe the same dust column as the extinction curve. We compare the properties of the SMC and LMC extinction curves with the CCM relationship three different ways: each curve by itself, the behavior of extinction at different wavelengths with R_V, and behavior of the extinction curve FM fit parameters with R_V. As has been found previously, we find that a small number of LMC extinction curves are consistent with the CCM relationship, but majority of the LMC and all of the SMC curves do not follow the CCM relationship. For the first time, we find that the CCM relationship seems to form a bound on the properties of all of the LMC and SMC extinction curves. This result strengthens the picture of dust extinction curves exhibit a continuum of properties between those found in the Milky Way and the SMC Bar. (abridged)Comment: 18 pages, 10 figures, ApJ in pres