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Critical Properties of Dimers, Spin Chains and Interface Models

Abstract : The study carried in this thesis concerns classical and quantum critical phenomena. Indeed, critical behaviors and phase transitions are fundamental topics in modern statistical physics and field theory and we propose in this thesis to study some models which exhibit such behaviors both at equilibrium and out of equilibrium. In the first part of the thesis, some properties of the two-dimensional dimer model are studied. This model has been studied extensively in the statistical physics and mathematical communities and a lot of applications in condensed matter physics exist. Here we propose to focus on exact solutions of the model and conformal invariance in order to have a deep understanding of this model in presence of monomers, and/or boundaries. The same kind of tools are then used to explore another important phenomenon appearing in dimer models and spin chains: the arctic circle. The goal was to find a proper field theoretical description of this phenomenon using exact solutions and asymptotic analysis. The second part of the thesis concerns out of equilibrium critical phenomena in the context of interface growth models. This field of research is very important nowadays, mainly because of the Kardar-Parisi-Zhang equation and its relations with random matrix ensembles. The phenomenology of these models in presence of boundaries is studied via exact solutions and numerical simulations, we show that surprising behaviors appear close to the boundaries
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Submitted on : Friday, March 30, 2018 - 9:50:11 AM
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Nicolas Allegra. Critical Properties of Dimers, Spin Chains and Interface Models. Other [cond-mat.other]. Université de Lorraine, 2015. English. ⟨NNT : 2015LORR0203⟩. ⟨tel-01754462⟩



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