This PhD thesis focuses on the mutual interplay of frustration and quenched disorder in magnetic insulators. Frustrated quantum magnets are known to host a plethora of interesting many-body phenomena ranging from noncollinear N\'el ordering to spin liquid phases. In this thesis, the consequences of the breakdown of translation symmetry, a widely occurring phenomenon in real materials, are studied in several examples of frustrated spin systems. The thesis is split into two parts dedicated to different kinds of frustrated magnets and the effects of quenched random perturbations in them. In the first part, bond randomness in frustrated noncollinear ordering is considered. Noncollinear magnetic orders originating from the spontaneous breakdown of continuous spin rotation symmetries at zero temperature are found to be unstable in the presence of exchange randomness. It is shown that in this case, the frustrated N\'{e}el ordering is destroyed for any magnitude of random exchange disorder. The resulting disordered ground states, however, possess interesting distinctions depending on the precise nature of the broken spin rotation symmetry. For SU(2) Heisenberg spins, it is demonstrated that the weak disordered ground describes a classical spin glass at zero temperature with a finite correlation length. At higher disorder, enhanced quantum fluctuations are predicted to modify that ground state into a random-singlet-like form. On the other hand, for noncollinear XY spin systems with U(1) or SO(2) symmetry which have stable integer-valued vortex topological defects, it is instead found that the weak disorder and the strong disorder ground states are distinct even at the classical level. The former has a quasi-long range order spin arrangement, while the latter exhibits a truly short-range ordered state. These two phases are shown to be separated by a Kosterlitz-Thouless-like phase transition point where vortex unbinding takes place. The spontaneously broken chiral degeneracy of noncollinear N\'el ordering is witnessed to be robust up to the point of the vortex-driven phase transition. In the second part of the thesis, the focus is switched to the effects of quenched disorder on quantum spin liquids. These are quantum disordered phases of matter with long-range entanglement, topological order, and fractionalised excitations that often arise in frustrated spin systems. The U(1) Dirac spin liquid with its magnetic monopole excitations has been identified as a parent state for N\'{e}el, valence-bond solid, and algebraic spin liquid phases. In this thesis, the fate of this state is studied in the presence of quenched random perturbations. It is demonstrated that a wide class of random perturbations induce monopole-driven confinement of the fractionalised quasi-particles of the spin liquid, leading to the onset of a spin glass-like order. Finally, dilution effects in the $\rm Z_2$ spin liquid phase of the Kitaev model are discussed in the presence of generic symmetry allowed interactions. The spin-liquid state remains stable when the non-Kitaev perturbations and dilution are small. However, the low-energy properties of the ground state are altered. It is shown that the degeneracies from the Majorana zero modes, which are known to localise at defect sites of the Kitaev spin liquid, are generically lifted by the non-Kitaev perturbations. Consequently, a dilution-tuned impurity band with a finite density of states is found to emerge.

Dans cette thèse, on étudie des processus stochastiques issus de la physique statistique. Le mouvement Brownien fractionnaire, objet central des premiers chapitres, généralise le mouvement Brownien aux cas où la mémoire est importante pour la dynamique. Ces effets de mémoire apparaissent par exemple dans les systèmes complexes et la diffusion anormale. L’absence de la propriété de Markov rend difficile l’étude probabiliste du processus. On développe une approche perturbative autour du mouvement Brownien pour obtenir de nouveaux résultats, sur des observables liées aux statistiques des extrêmes. En plus de leurs applications physiques, on explore les liens de ces résultats avec des objets mathématiques, comme les lois de Lévy et la constante de Pickands. / In this thesis, we study stochastic processes appearing in different areas of statistical physics: Firstly, fractional Brownian motion is a generalization of the well-known Brownian motion to include memory. Memory effects appear for example in complex systems and anomalous diffusion, and are difficult to treat analytically, due to the absence of the Markov property. We develop a perturbative expansion around standard Brownian motion to obtain new results for this case. We focus on observables related to extreme-value statistics, with links to mathematical objects: Levy’s arcsine laws and Pickands’ constant. Secondly, the model of elastic interfaces in disordered media is investigated. We consider the case of a Brownian random disorder force. We study avalanches, i.e. the response of the system to a kick, for which several distributions of observables are calculated analytically. To do so, the initial stochastic equation is solved using a deterministic non-linear instanton equation. Avalanche observables are characterized by power-law distributions at small-scale with universal exponents, for which we give new results.

De nombreux systèmes complexes soumis à un ajout continu d'énergie réagissent à cet ajout par une accumulation de tension au cours du temps, interrompue par de soudaines libérations d'énergie appelées avalanches. Récemment, il a été remarqué que plusieurs propriétés élémentaires de la dynamique d'avalanche sont issues de processus de relaxation ayant lieu à une échelle microscopique, processus qui sont négligés dans la plupart des modèles. Lors de ma thèse, j'ai étudié deux modèles classiques d'avalanches, modifiés par l'ajout d'une forme de relaxation la plus simple possible. Le premier système est une interface viscoélastique tirée à travers un milieu désordonné. En champ moyen, nous prouvons que l'interface a un comportement périodique caractérisé par une nouvelle échelle temporelle (émergente), avec des avalanches qui touchent l'ensemble du système. Le calcul semi-analytique de la force de friction agissant sur la surface donne des résultats compatibles avec les expériences de friction classique. En dimension finie (2D), les événements touchant l'ensemble du système (trouvés en champ moyen) deviennent localisés, et les simulations numériques donnent des résultats en bon accord avec plusieurs caractéristiques importantes des tremblements de terre, tant qualitativement que quantitativement. Le second système incluant également une forme très simple de relaxation est un modèle jouet d'avalanche : c'est la percolation dirigée. Dans notre étude d'une variante non-markovienne de la percolation dirigée, nous avons observé que la classe d'universalité était modifiée mais seulement partiellement. En particulier, un exposant change de valeur tandis que plusieurs relations d'échelle sont préservées. Cette idée d'une classe d'universalité étendue, obtenue par l'ajout d'une perturbation non-markovienne offre des perspectives prometteuses pour notre premier système. / Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, which are neglected by most models. During my thesis, I studied two well-known models of avalanche dynamics, modified minimally by the inclusion of some forms of relaxation. The first system is that of a viscoelastic interface driven in a disordered medium. In mean-field, we prove that the interface has a periodic behaviour (with a new, emerging time scale), with avalanche events that span the whole system. We compute semi-analytically the friction force acting on this surface, and find that it is compatible with classical friction experiments. In finite dimensions (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results in good agreement with several important features of real earthquakes. The second system including a minimal form of relaxation consists in a toy model of avalanches: the Directed Percolation process. In our study of a non-Markovian variant of Directed Percolation, we observed that the universality class was modified but not completely. In particular, in the non-Markov case an exponent changes of value while several scaling relations still hold. This picture of an extended universality class obtained by the addition of a non-Markovian perturbation to the dynamics provides promising prospects for our first system.

This thesis presents a series of studies of quenched random disorder (QRD) on liquid crystals. We have used high-resolution AC-Calorimetry, high-resolution X-Ray Diffraction (XRD), X-Ray Intensity Fluctuation Spectroscopy (XIFS), Turbidity, Integrated Low-Angle Light Scattering (ILALS), as well as Polarizing Microscopy to characterize the effects of a nano-colloidal dispersions of aerosils in the phase transitions of several liquid crystals. The aerosil ($SIL$) is made of 70~AA~ diameter SiO$_{2}$ particles coated with hydroxyl (-OH) groups. The coating allows the $SIL$ particles to hydrogen-bond together, to form a very low density gel in an organic solvent. This provides the quenched random disorder. The liquid crystals of interest are: octyloxycyanobiphenyl ($8OCB$), 4-extit{n}-pentylphenylthiol-4'-extit{n}-octyloxybenzoate (ar{8}$S5), 4'-transbutyl-4-cyano-4-heptyl-bicyclohexane ($CCN47$), and octylcyanobiphenyl ($8CB$). Studies have been carried out as a function of aerosil concentration and temperature spanning the following phase transitions, Isotropic to Nematic (emph{I-N}), nematic to smectic-emph{A} (emph{N-SmA}), smectic-emph{A} to smectic-emph{C} (emph{SmA-SmC}), and crystallization.

Comprehension of eruptive histories is critical in understanding the evolution of magmatic systems at arc volcanoes and may supply evidence to the petrogenesis of intermediate and evolved magmas. Within the 300 ka eruptive history of Mount St. Helens, Washington, the Kalama Eruptive Period, 1479- ~1750 CE was bracketed by interludes of quiescence (Hoblitt et al., 1980) and thus likely represents an entire eruptive cycle within a span of 300 years. Study of the magmatic evolution during this short time period provides key information regarding inputs and the plumbing system of Mount St. Helens. This research aims to enhance comprehension of processes leading to the petrogenesis of intermediate magmas by providing whole rock and phase geochemical data of an eruptive cycle, thereby providing constraints on the magmatic evolution of the Kalama Eruptive Period. The eruptive sequence is divided into early, middle and late subperiods. The early Kalama began with two dacitic plinian eruptions and continued with smaller eruptions of dacite domes (64.4-66.5 wt% SiO₂) that included quenched mafic inclusions (53.7-57.7 wt% SiO₂). The middle Kalama signified the onset of basaltic andesite and andesite eruptions ranging between 55.5-58.5 wt % SiO₂. Subsequently, summit domes that began as felsic andesite (61-62.5 wt% SiO₂) and transitioned to dacite (62.5-64.6 wt% SiO₂) dominated the late Kalama. Previous work on Kalama-aged rocks suggests magma mixing is an integral process in their production. Compositions and textures of crystal phases, in addition to the presence of xenocrysts in middle and late Kalama rocks, confirm mechanical mixing of magmas likely produced many of the sampled compositions. New petrographic observations were integrated with new whole rock and phase EMP and LA-ICP-MS data and the known stratigraphy in order to constrain the magmatic and crustal components active during the Kalama Eruptive Period. New findings include: 1. Two populations of quenched mafic inclusions, one olivine-rich and one olivine-poor, are identified from the early Kalama based on mineralogy, textures, and major and trace element chemistry. Major element modeling shows crustal anatexis of plutonic inclusions found in early Kalama dacites could produce the felsic magma source of the olivine-poor population. The olivine-rich population incorporated cumulate material. 2. Four distinct lava populations erupted during the early part of the middle Kalama (X lavas), including two found exclusively in lahar deposits: M-type lahars are the most mafic, B-type lahars are more mixed, the Two Finger Flow was previously grouped with other middle Kalama-age lavas, and the X lava (in situ) has unique geochemical and textural character. X tephras likely correlate with the lavas. 3. There were at least three mafic source contributions at Mount St. Helens during the eruptive period: the parent to the X deposits, the cumulate material in the olivine-rich QMIs, and the calc-alkaline parent to the MKLV and SDO. The magma reservoir at Mount St. Helens has been modeled as a single, elongate chamber (Pallister et al., 1992). Multiple coeval basaltic or basaltic andesite parents fluxing into the magmatic system beneath the volcano could indicate a more complex magma chamber structure. / Graduation date: 2011

Die Wirkung nichtmetallischer Einschlüsse auf das temperatur- und beanspruchungsratenabhängige Festigkeits-, Verformungs- und Zähigkeitsverhalten des Stahls G42CrMo4 wird erforscht. Die im Rahmen des SFB 920 entwickelten Filter mit funktionalisierter Oberfläche dienten der Reinigung einer vorher bewusst verunreinigten Stahlschmelze. Diese Stähle werden mit kommerziell verfügbaren Stählen verglichen. Das Festigkeits- und Verformungsverhalten wird durch bekannte Modelle beschrieben, um das Zähigkeitsverhalten zu analysieren. Die Messung der bei schlagartiger Beanspruchung und tiefer Temperatur geringeren Zähigkeit erfolgt durch methodisch weiter- und neuentwickelte Versuchsaufbauten. Die geringere Zähigkeit der Stähle, die im Rahmen des SFB 920 hergestellt wurden, wird auf den höheren Einschlussanteil zurückgeführt. Das Zähigkeitsverhalten wird durch ein neues Modell beschrieben, das die fraktographisch ermittelte Einschlussverteilung einbezieht.

We have developed a new modulation calorimetry technique using RF-Field heating. This technique eliminates temperature gradients across the sample leading to a higher precision in evaluating the heat capacity compared to the previous techniques. A frequency scan was carried out on a 8CB+aerosil sample showing a wide plateau indicating the region of frequency independent heat capacity. A temperature scan was then performed through the first-order nematic to isotropic and second order smectic-A to nematic transitions and was shown to be consistent with the previous work. The amplitude of the RF heating power applied to the sample depends on the permittivity and the loss factor of the sample. Since the permittivity of a dielectric material has a strong temperature dependence in liquid crystals, new information is obtained. The heat capacity measurements have a relative resolution of better than 0.06%, and the phase shift a resolution of 0.03%, were shown to be significant improvements over traditional heating methods. We then applied this new RF calorimetry on bulk and aerosil 8CB dispersions. For the bulk 8CB, the step-like character of smectic-A to nematic transition, and first order nematic to isotropic transitions indicated the strong dominance of the permittivity and the loss factor of the material. For the 8CB+aerosil samples at different silica density, our data were consistent with the previous work and provides clear evidence for the coupling between the smectic-A and nematic phases. We have undertaken a combined T-dependent optical and calorimetric investigation of CCN47+aerosil samples through the I-N transition over a range of silica densities displaying the double I-N transition peak. This work offers compelling evidence that the I-N transition with weak quenched random disorder proceeds via a two-step process in which random-dilution is followed by random-field interactions on cooling from the isotropic phase, a previously unrecognized phenomena.