Interactions in Quasicrystals

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in {\it periodic} crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in {\it quasicrystalline} structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.Comment: Proceedings of the Many Body X conference (Seattle, Sept. 99); 9 pages; uses epsfi

Dielectric properties of aqueous electrolytes at the nanoscale

Despite the ubiquity of nanoconfined aqueous electrolytes, a theoretical framework that accounts for the nonlinear coupling of water and ion polarization is still missing. We introduce a nonlocal and nonlinear field theory for the nanoscale polarization of ions and water and derive the electrolyte dielectric properties as a function of salt concentration to first order in a loop expansion. Classical molecular dynamics simulations are favorably compared with the calculated dielectric response functions. The theory correctly predicts the dielectric permittivity decrement with rising salt concentration and furthermore shows that salt induces a Debye screening in the longitudinal susceptibility but leaves the short-range water organization remarkably unchanged.Comment: 6 pages, 3 figure

Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear in Phys.Rev.

Interacting fermions in self-similar potentials

We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.Comment: 18 pages, 10 EPS figure

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

Une approche du groupe de renormalisation nonperturbatif aux membranes polymérisées

In this thesis, we study the long-range behaviour of polymerized membranes using a non-perturbative renormalization group (NPRG) approach. We start by presenting the NPRG after which we introduce membrane systems. In our work, we concentrate on polymerized membranes of different types: homogeneous, anisotropic and quenched disordered. Moreover as a side project, we work on Lifshitz critical behaviour (LCB) in magnetic systems. Our results, both for polymerized membranes and LCB, compare well with weak-coupling, low-temperature and large-d (or large-n for LCB) perturbative results in the limiting cases. But more importantly the need of a non-perturbative approach is justified by the fact that the physically interesting cases have been difficult to compute. A long-standing question in homogeneous membranes is the order of the transition between the crumpled and flat phases. Although we do not have a definite answer, our results seem to indicate that the transition is first order in agreement with recent Monte Carlo simulations. An interesting feature of homogeneous membranes is the existence of the flat phase at low-temperature with a non-trivial behaviour. This flat phase has shown to correctly describe the behaviour of graphene although the electronic degrees of freedom are not taken into accountDans cette thèse, nous étudions le comportement à longue distance des membranes polymérisées en utilisant une approche de groupe de renormalization non-perturbative (NPRG). Après une présentation du NPRG, nous introduisons les membranes. Dans notre travail, nous nous concentrons sur différents types de membranes polymérisées: homogène, anisotrope et avec du désordre gelé. De plus, nous avons aussi étudié les points de Lifshitz dans les systèmes magnétiques. Nos résultats, aussi bien pour les membranes que pour Lifshitz, se comparent bien aux résultats perturbatifs dans les différents cas limites: couplages faibles, basse température et large-d (ou large-n pour Lifshitz). Mais, en utilisant le NPRG, nous pouvons aller au de-là de ces cas limites et atteindre les cas qui sont physiquement intéressants. La question de l'ordre de la transition entre la phase froissé et la phase plate dans les membranes homogènes est depuis longtemps sans une réponse définitive. Malgrè que nos résultats ne permettent pas encore de lever cette question, ils semblent indiquer que la transition est du premier ordre en accord avec des simulations récentes. Une propriété importante des membranes polymérisées est l'existence d'une phase plate à basse température avec un comportement non-trivial. Cette phase décrit correctement le comportement du graphène malgrè que les dégrées de liberté électroniques ne soient pas pris en comptePARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF

Phase diagram and criticality of the random anisotropy model in the large- N limit

International audienceWe revisit the thermodynamic behavior of the random-anisotropy O(N) model by investigating its large-N limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-N limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible “glassy” phases. Finally we discuss the implications of our findings for the finite-N and finite-temperature systems

Une approche non perturbative de systèmes frustrés et de systèmes désordonnés

PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF