A topological invariant of RG flows in 2D integrable quantum field theories

We construct a topological invariant of the renormalization group trajectories of a large class of 2D quantum integrable models, described by the thermodynamic Bethe ansatz approach. A geometrical description of this invariant in terms of triangulations of three-dimensional manifolds is proposed and associated dilogarithm identities are proven.Comment: 12 pages, 6 figures. Presented at the Euroconference on New Symmetries in Statistical Mech. and Cond. Mat. Physics, Torino, July 20- August 1 1998. typos correcte

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

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes

Gauged O(n) spin models in one dimension

We consider a gauged O(n) spin model, n >= 2, in one dimension which contains both the pure O(n) and RP(n-1) models and which interpolates between them. We show that this model is equivalent to the non-interacting sum of the O(n) and Ising models. We derive the mass spectrum that scales in the continuum limit, and demonstrate that there are two universality classes, one of which contains the O(n) and RP(n-1) models and the other which has a tuneable parameter but which is degenerate in the sense that it arises from the direct sum of the O(n) and Ising models.Comment: 9 pages, no figures, LaTeX sourc

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

Universality Class of O(N)O(N) Models

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta=1/4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta=\pi$.Comment: 8 pages, with 3 figures included, postscript. An error concerning the errors has been correcte

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