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

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

Steady States of a Nonequilibrium Lattice Gas

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase, and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.Comment: 14 pages, 24 figure

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

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

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

Testing fixed points in the 2D O(3) non-linear sigma model

Using high statistic numerical results we investigate the properties of the O(3) non-linear 2D sigma-model. Our main concern is the detection of an hypothetical Kosterlitz-Thouless-like (KT) phase transition which would contradict the asymptotic freedom scenario. Our results do not support such a KT-like phase transition.Comment: Latex, 7 pgs, 4 eps-figures. Added more analysis on the KT-transition. 4-loop beta function contains corrections from D.-S.Shin (hep-lat/9810025). In a note-added we comment on the consequences of these corrections on our previous reference [16

Statistical mechanics of glass transition in lattice molecule models

Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An infinite series of irregular ground states are constructed theoretically. By defining a glass order parameter as a collection of the overlap with each ground state, a thermodynamic transition to a glass phase is found in a stratified Wang tiles model on a cubic lattice.Comment: 18 pages, 8 figure

New Universality Classes for Two-Dimensional σ\sigma-Models

We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for $N=3,4$ on lattices up to $512 \times 512$, using a Wolff-type embedding algorithm. [CPU time $\approx$ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the $RP^{N-1}$ and $N$-vector models do not lie in the same universality class.Comment: 10 pages (includes 2 figures), 211176 bytes Postscript, NYU-TH-93/07/03, IFUP-TH 34/9

Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice

We present a high-statistics Monte Carlo determination of the exponent gamma for self-avoiding walks on a Manhattan lattice in two dimensions. A conservative estimate is \gamma \gtapprox 1.3425(3), in agreement with the universal value 43/32 on regular lattices, but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations. We find strong corrections to scaling that seem to indicate the presence of a non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma = 1.3436(3), where the error is purely statistical.Comment: 24 pages, LaTeX2e, 4 figure