Critical Properties of Dimers, Spin Chains and Interface Models

• Main Author: Allegra, Nicolas
• Other Authors: Institut Jean Lamour (IJL), Institut de Chimie du CNRS (INC)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Université de Lorraine, Malte Henkel, Jean-Yves Fortin
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: HAL CCSD 2015
• Subjects: Critical phenomena; Dimer models; Grassmann algebra; Conformal invariance; Spin chains; Out of equilibrium statistical physics; Interface growth; KPZ equation; Phénomènes critiques; Modèles de dimères; Algèbre de Grassmann; Invariance conforme; Physique statistique hors-équilibre; Croissance d’interface; Équation de KPZ; Dimères; Physique statistique; Transitions de phases; Phénomènes critiques (physique); Équations aux dérivées partielles stochastiques; Invariants conformes; [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]; Arctic
• Online Access: https://hal.univ-lorraine.fr/tel-01754462; https://hal.univ-lorraine.fr/tel-01754462/document; https://hal.univ-lorraine.fr/tel-01754462/file/DDOC_T_2015_0203_ALLEGRA.pdf

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 L’étude réalisée dans cette thèse porte sur les phénomènes critiques classiques et quantiques. En effet, les phénomènes critiques et les transitions de phases sont devenus des sujets fondamentaux en physique statistique moderne et en théorie des champs et nous proposons dans cette thèse d’étudier certains modèles qui présentent un comportement critique, à la fois à l’équilibre et hors de l’équilibre. Dans la première partie de la thèse, certaines propriétés du modèle de dimères à deux dimensions sont étudiées. Ce modèle a été largement étudié dans les ...