Stuttgart, Univ., Diss., 2008.

Hamburg, University, Diss., 2000.

Hamburg, University, Diss., 2004.

Une décennie après la découverte du graphème par A.K. Geim et K.S. Novoselov ,beaucoup de ses propriétés fondamentales ont été intensément étudiées. En effet, lespromesses du graphème a été etenues et ont conduit a une recherche fructueuse dansdes domaines aussi varies que l'optique, la mécanique, la chimie ou l'électronique. Legraphème mérite ainsi d'être appelée le matériau miracle puisque c'est un très conducteurde la chaleur et de l'électricité, il est l'un des matériau les plus solides tout en étantléger et optiquement transparent. Son succès est en partie dû à la technique de micro clivage,ou exfoliation qui est facile et accessible à tout laboratoire sans équipementlourd. Cela a permis d'étudier les propriétés du graphème avec un large éventail de techniquesexpérimentales. Après l'immense succès du graphème, d'autres matériaux bidimensionnels(2D) ont été obtenus avec la même technique, conduisant à une physiqueparticulièrement riche. / A decade after the discovery of grapheme by A.K. Geim and K.S. Novoselov , manyof its fundamental properties have been intensely studied. Indeed, the early promise ofgrapheme has been kept, leading to a fruitful research in many felds as diverse as optics,mechanics, chemistry or electronics, and grapheme still deserves the name of wondermaterial as among its attributes there is an exceptionally good conduction of heat andelectricity, it is one of the strongest known material while being light and opticallytransparent. Its success was partly due to the easy micromechanical cleavage or scotchtape exfoliation technique accessible to any laboratory without heavy equipment, thatallowed to study the properties of grapheme with a wide range of experimental techniques.Following the success of grapheme, other two-dimensional (2D) materials were obtainedwith the same technique, leading to a particularly rich physics.

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<p>The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.</p><p>In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.</p> / Dissertation