Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional NN-Vector Model for N=3,4,8N=3,4,8

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.Comment: 68456 bytes uuencoded gzip'ed (expands to 155611 bytes Postscript); 4 pages including all figures; contribution to Lattice '9

Lattice energy-momentum tensor with Symanzik improved actions

We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the sigma model they can have applications in Monte Carlo simulations.Comment: Self extracting archive fil

The W1+∞W_{1 + \infty } effective theory of the Calogero- Sutherland model and Luttinger systems.

We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles $N$. It is given by a \winf conformal field theory (with central charge $c=1$) that describes {\it exactly} the spatial density fluctuations arising from the low-energy excitations about the Fermi surface. Our approach does not rely on the integrable character of the model, and indicates how to extend previous results to any order in powers of $1/N$. Moreover, the same effective theory can also be used to describe an entire universality class of $(1+1)$-dimensional fermionic systems beyond the Calogero-Sutherland model, that we identify with the class of {\it chiral Luttinger systems}. We also explain how a systematic bosonization procedure can be performed using the \winf generators, and propose this algebraic approach to {\it classify} low-dimensional non-relativistic fermionic systems, given that all representations of \winf are known. This approach has the appeal of being mathematically complete and physically intuitive, encoding the picture suggested by Luttinger's theorem.Comment: 13 pages, plain LaTeX, no figures

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

On the question of universality in \RPn and \On Lattice Sigma Models

We argue that there is no essential violation of universality in the continuum limit of mixed \RPn and \On lattice sigma models in 2 dimensions, contrary to opposite claims in the literature.Comment: 16 pages (latex) + 3 figures (Postscript), uuencode

The extended conformal theory of the Calogero-Sutherland model

We describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented.Comment: 12 pages, plain LaTeX, no figures; To appear in the proceedings of the IV Meeting "Common Trends in Condensed Matter and High Energy Physics", Chia Laguna, Cagliari, Italy, 3-10 Sep. 199

Selberg integrals in 1D random Euclidean optimization problems

We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points $x$ and $y$ is the Euclidean distance between them to an arbitrary power $p\ge1$, and the points are chosen at random with flat measure. We derive the exact average cost for the random assignment problem, for any number of points, by using Selberg's integrals. Some variants of these integrals allows to derive also the exact average cost for the bipartite travelling salesman problem.Comment: 9 pages, 2 figure

New Method for the Extrapolation of Finite-Size Data to Infinite Volume

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $\sigma$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.Comment: 3 pages, 76358 bytes Postscript, contribution to Lattice '94; see also hep-lat/9409004, hep-lat/9405015 and hep-lat/941100