Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. and are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites consituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. We analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (``$n$-legged animals'') in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain.Comment: 10 pages, 6 figures, LaTeX document class EP

Magnetic properties of the three-dimensional Hubbard model at half filling

We study the magnetic properties of the 3d Hubbard model at half-filling in the TPSC formalism, previously developed for the 2d model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with Dynamical Mean-Field results for the isotropic 3d model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3d case, and the 2d or anisotropic 3d cases for the double occupation factor. Even for this local correlation function, 2d or anisotropic 3d cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.Comment: RevTex, 9 pages +10 figure

Transitions de phase dans les monocouches de lécithines aux interfaces eau-air : un modèle thermodynamique

En s’appuyant sur de récents travaux expérimentaux, nous proposons un modèle visant à décrire le comportement des monocouches de lécithine déposées sur une interface eau-air. Une des principales caractéristiques de ces molécules est leur cosurface anisotrope dans le plan de l’interface. De plus, elles possèdent une tête polaire interagissant fortement avec l’eau. Ces deux propriétés sont prises en compte dans notre modèle où nous représentons les molécules par des rectangles (munis d’une tête polaire) distribués sur un réseau carré. Nous obtenons différentes phases dont une phase nématique bidimensionnelle et une phase où les têtes polaires s’ordonnent, donnant alors une structure hexagonale pour les chaînes. Ces différentes phases sont analogues à celles trouvées par les expérimentateurs en référence