Four-loop contributions to long-distance quantities in the two-dimensional nonlinear sigma-model on a square lattice: revised numerical estimates

We give the correct analytic expression of a finite integral appearing in the four-loop computation of the renormalization-group functions for the two-dimensional nonlinear sigma-model on the square lattice with standard action, explaining the origin of a numerical discrepancy. We revise the numerical expressions of Caracciolo and Pelissetto for the perturbative corrections of the susceptibility and of the correlation length. For the values used in Monte Carlo simulations, N=3, 4, 8, the second perturbative correction coefficient of the correlation length varies by 3%, 4%, 3% respectively. Other quantities vary similarly.Comment: 2 pages, Revtex, no figure

Multicanonical Study of the 3D Ising Spin Glass

We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite size scaling, as well as the zero temperature limit to explore the ground state properties.Comment: FSU-SCRI-92-121; 7 pages; sorry, no figures include

The two-phase issue in the O(n) non-linear σ\sigma-model: A Monte Carlo study

We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.Comment: 3 pgs. espcrc2.sty included. Talk presented at LATTICE96(other models

General duality for abelian-group-valued statistical-mechanics models

We introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set of ``interactions''. A Gibbs factor is associated to each variable and to each interaction. We introduce a duality transformation for systems in this class. The duality exchanges the abelian group with its dual, the Gibbs factors with their Fourier transforms, and the interactions with the variables. High (low) couplings in the interaction terms are mapped into low (high) couplings in the one-body terms. The idea is that our class of systems extends the one for which the classical procedure 'a la Kramers and Wannier holds, up to include randomness into the pattern of interaction. We introduce and study some physical examples: a random Gaussian Model, a random Potts-like model, and a random variant of discrete scalar QED. We shortly describe the consequence of duality for each example.Comment: 26 pages, 2 Postscript figure

Dynamic Critical Behavior of an Extended Reptation Dynamics for Self-Avoiding Walks

We consider lattice self-avoiding walks and discuss the dynamic critical behavior of two dynamics that use local and bilocal moves and generalize the usual reptation dynamics. We determine the integrated and exponential autocorrelation times for several observables, perform a dynamic finite-size scaling study of the autocorrelation functions, and compute the associated dynamic critical exponents $z$. For the variables that describe the size of the walks, in the absence of interactions we find $z \approx 2.2$ in two dimensions and $z\approx 2.1$ in three dimensions. At the $\theta$-point in two dimensions we have $z\approx 2.3$.Comment: laTeX2e, 32 pages, 11 eps figure

Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model

By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough lattices to have a good control on finite-size effects. The magnetic susceptibility and three different definitions of the correlation length are measured. We check our results with large-n expansions as well as with standard formulae for asymptotic freedom up to 4 loops in the standard and effective schemes. For this purpose the weak coupling expansions of the energy up to 4 loops for the standard action and up to 3 loops for the Symanzik action are calculated. For the O(3) model we have used two different effective schemes and checked that they lead to compatible results. A great improvement in the results is obtained by using the effective scheme based on the energy at 3 and 4 loops. We find that the O(8) model follows very nicely (within few per mille) the perturbative predictions. For the O(3) model an acceptable agreement (within few per cent) is found.Comment: latex source + 15 e-postscript figures. It generates 26 pgs. Replaced version containing more corrections to scaling for the Symanzik action, more detailed explanation of the calculation of $C_\chi$ and a few more citation

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Causal Propagators for Algebraic Gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.Comment: LaTex, 09 pages, no figure

A General Limitation on Monte Carlo Algorithms of Metropolis Type

We prove that for any Monte Carlo algorithm of Metropolis type, the autocorrelation time of a suitable ``energy''-like observable is bounded below by a multiple of the corresponding ``specific heat''. This bound does not depend on whether the proposed moves are local or non-local; it depends only on the distance between the desired probability distribution $\pi$ and the probability distribution $\pi^{(0)}$ for which the proposal matrix satisfies detailed balance. We show, with several examples, that this result is particularly powerful when applied to non-local algorithms.Comment: 8 pages, LaTeX plus subeqnarray.sty (included at end), NYU-TH-93/07/01, IFUP-TH33/9

Random Walks with Long-Range Self-Repulsion on Proper Time

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included) IFUP-Th 13/92 and SNS 14/9